sw00888math--DFnote-and-squares-da-patterns

32


 DF = Descension Family          da = digit addition
 nnss = natural number summation sequence

 DF note:  As God would have it, when I began unstacking the high
pile of manilla folders holding writings of mine from my computer stool,
the first group did not separate as normal, revealing a sheet of lined
paper on which I had penned some math thoughts on 7-31-06.  I let
it be and moved what I held/ over to its usual location on my bed.
Later, I read what I'd noted, and found it of interest in one particular
way: an nDF descends to a value which is n - 1.  If n = 10 (5 x 5),
then (5 + 5) - 1 = the final resultant for 10DF.  This formula is not in
the note, but the note's examples imply it.

My project today is a continuation of the da patterns for the decades
pertaining to odd squares, and possibly to even squares.  Want to be
more explicit, and want to investigate if and where intersectings occur.
-
First, a brief review:  The 2 5 8 pattern for the only group in which
paired twin primes can be found looks like this:
[ Insert:  Decade # equals (decade's f-d-5 integer plus 5) divided by 10. 
   Example: (15 + 5)/10 = 2 ]
2  5  8  -  15/3 = 5 (5)          45/3 = 15 (6)          75/3 = 25 (7)                     
2  5  8  -  105/3 = 35 (8)          135/3 = 45 (9)          165/3 = 55 (1)               
[ Insert:  The 2nd row decades are 11 (2), 14 (5), 17 (8). ]
2  5  8  -  195/3 = 65 (2)          225/3 = 75 (3)          255/3 = 85 (4)               
2  5  8  -  285/3 = 95 (5)          315/3 = 105 (6)          345/3 = 115 (7)           
2  5  8  -  375/3 = 125 (8)          405/3 = 135 (9)          435/3 = 145 (1)          
2  5  8  -  465/3 = 155 (2)          495/3 = 165 (3)          525/3 = 175 (4)          
:
[ Insert:  Have decided to use the f-d-5 integers for the f-d-1 and f-d-9 groups. ]
1  9  4  -  [1] 5/3 = 1.6 (1)    [81] 85/3 = 28.3 (9)    [121] 125/3 = 41.6 (4)    
1  9  4  -  [361] 121.6 (1)    [441] 148.3 (9)    [841] 281.6 (4)                      
7  9  7  -  [961] 321.6 (7)    [1521] 508.3 (9)    [1681] 561.6 (7)                   
7  9  7  -  [2401] 801.6 (7)    [2601] 868.3 (9)    [3481] 1161.6 (7)                
4  9  1  -  [3721] 1241.6 (4)    [4761] 1588.3 (9)    [5041] 1681.6 (1)             
4  9  1  -  [6241] 2081.6 (4)    [6561] 2188.3 (9)    [7921] 2641.6 (1)             
:
1  5  8  -  [9] 1.6 (9)          [49] 15 (4)          [169] 55 (7)                           
2  8  1  -  [289] 95 (1)          [529] 175 (7)          [729] 241.6 (9)                 
1  2  5  -  [1089] 361.6 (9)          [1369]455 (1)          [1849] 615 (4)
5  2  1  -  [2209] 735 (4)          [2809] 935 (1)          [3249] 1081.6 (9)         
1  8  2  -  [3969] 1231.6 (9)      [4489] 1495 (7)      [5329] 1775 (1)              
8  5  1  -  [5929] 1975 (7)      [6889] 2295 (4)      [7569] 2521.6 (9)               

In the first group's first column is a 95.  In the third group's first column is a 95.
That says the same decade is being referenced in both.  That decade is 29.
That says 289 is a square and therefore decade 29 is eliminated.  This is what
I mean by intersectings.

More to come.

PM 2:24 - I don't do math the way professional mathematicians do;
yet I strive to be rigorous.  Ideally, I would like to be able to ascertain
all the essential qualities of an integer just by closely observing it.  I am
seeking methods which will apply into infinity, but I prefer methods 
which do not require intricate formulas.
Of the 18 terms in the first cycle of the f-d-9 group, 12 intersect with
terms in group 1.  Of the 18 terms in the first cycle of the f-d-1 group,
0 instersect with terms in group 1.  Of those that interact, four are of
the da2 kind, four of the da5, and four of the da8.  The square in the
first da5 is 49, and the square in the first da8 is 169.  In groups 2 and
3 the order is irregular within each cycle, but does have a pattern.  In
group 1 the order is regular, but group 1's order does not depend on
where square's occur but rather on where "3" divides evenly into an
f-d-5 integer.  In group 2 "3" does not divide evenly into any f-d-5
integer.  In group 3 "3" divides evenly into an f-d-5 integer 12 times
in each 18-term cycle.  In group 3 the first da8 is in R1C3, but in the
first group it is in R2C3.  What does this tell about what is in R1C3
in group 1?  That it does not have an f-d-9 square in it, but that some
other eliminator of a form not here being tested might be lurking there
remains a possibility.  I believe it's time for a different chart.

These are decade # / da charts:
-
Group 1
2 / 2          5 / 5          8 / 8
11 / 2          14 / 5          17 / 8
20 / 2          23 / 5          26 / 8
29 / 2          32 / 5          35 / 8
38 / 2          41 / 2          44 / 8
47 / 2          50 / 5          53 / 8
:
Group 3
1 / 1          5 / 5          17 / 8
29 / 2          53 / 8          73 / 1
109 / 1          137 / 2          185 / 5
221 /5281 / 2          325 / 1
397 / 1    449 / 8          533 / 2
593 / 8          689 / 5          757 / 1

After some figuring, figured out 689 / 5 in group 3 is in
R5C2 of cycle 13 in group 1, which cycle's 18th term is
701, there being a 54 spread in each cycle after cycle 1.
12 x 54 = 648; 648 + 53 = 701.  701, 698, 695, 692, 689.
(689 x 10) - 1 = 6889.

More to come.

05/16/08  AM 7:32  -  A little something that provides both an 
nnss magic number and the number to minus from and plus to it:
2 x 0 x 0 = 0    
2 x 1 x 1 = 2    2 x 2 x 2 = 8    2 x 3 x 3 = 18    2 x 4 x 4 = 32    2 x 5 x 5 = 50
2 x 6 x 6 = 72
for generating the natural number summation sequence:
0          
1    3          6    10          15    21          28    36          45    55          66    78
and dividing one of these magic numbers by "2" begets a square as with 50/2
-
a different view of these nnss magic numbers:
0          2          8          18          32          50          72
     2          6          10          14          18          22 
so
(4 x 0) + 2    (4 x 1) + 2    (4 x 2) + 2    (4 x 3) + 2    (4 x 4) + 2    (4 x 5) + 2
-
Also, as can be seen, I have separated the nnss into sets.
Adding the integers in a set gets an even square,
 and subtracting a set's lesser # from its greater # 
 gets the even square's square root.
Adding the integers between sets gets an odd square,
 and subtracting the lesser # from the greater # 
 gets the odd square's square root.
-
a way to allow the term position (tpo) of an nnss magic number 
 to equal the second and third square root associated with that number:
0's tpo is 0    2's tpo is 1    8's tpo is 2    18's tpo is 3    32's tpo is 4
Thus, for this sequence, tpo 3 = 2 x 3 x 3.    18 - 3 = 15    18 + 3 = 21
-
Another view of the squares:
0 1 2    3 4 5    8 9 10    15 16 17    24 25 26    35 36 37    48 49 50

During lunch break I uncovered digit addition relationships 
between square roots and their squares.  Examples follow:
1    1 = 1  1 = 1    19 = 1  361 = 1    28 = 1  784 = 1    73 = 1  5329 = 1
2    2 = 2  4 = 4    11 = 2  121 = 4    38 = 2  1444 = 4    47 = 2  2209 = 4
3    3 = 3  9 = 9    |    6 = 6  36 = 9    |    9 = 9  81 = 9
4    4 = 4  16 = 7    13 = 4  169 = 7    22 = 4  484 = 7    103 = 4  10609 = 7
5    5 = 5  25 = 7    14 = 5  196 = 7    23 = 5  529 = 7    41 = 5    1681 = 7
7    7 = 7  49 = 4    16 = 7  256 = 4    25 = 7  625 = 4    61 = 7  3721 = 4
8    8 = 8  64 = 1    17 = 8  289 = 4    26 = 8  676 = 4    71 = 8  5041 = 4
Note the 1 4 9 7 7 9 4 1 9 routine.  To start:  If a square root is of the 3, 6, or 9
variety, its square will be of the 9 variety as in 21 = 3  441 = 9.  Sqrts of the
4 and 5 variety net squares of the 7 variety.  Sqrts of the 2 and 7 variety net
squares of the 4 variety.  Sqrts of the 1 and 8 variety net squares of the 1 variety.
All this helps in that knowing the da of a square limits its possible square roots.
The square "6889" = 31 = 4 and so signals that its sqrt must be a da2 or a da7.
One is still left guessing, or trying other methods.  6888/4 = 1722    1722/3 = 574
574/7 = 82    3 x 4 x 7 = 84    82 x 84 = 6888    83 x 83 = 6889    83 = 11 = 2


May 17, 2008 note - Stating the implicit: Every nine integers.       






#
Brian A. J. Salchert

sw00887math--my-paired-twin-primes-proof

31


 is nothing fancy, but a bit complex.  The goal is to discern
how/where/why paired twin primes can be found.  Here is
a simple example using decade two.  (The first decade is:
0 1 2 3 4 5 6 7 8 9.)  (In a decade pattern scheme, decade
10 is actually a 1 because digit addition is used to determine
decade patterns.)

10   |   11      12      13      14      15      16      17      18      19

Note:  Only an integer whose final digit is "5" can be at the center of
a paired twin primes set because an integer whose final digit is "5"
will be encountered if the center is at an integer whose final digit is
"1" or "3" or "7" or "9" (11 + 4 = 15  13 + 2 = 15  17 - 2 = 15  19 - 4 = 15).

Step 1.  That integer whose final digit is "5" must be 
              evenly divisible by "3".
Step 2.  In the decade being investigated/ the integers
              whose final digits are "2" and "8" must be
              evenly divisible by "6".
Step 3.  Also, one of the integers noted in Step 2
              must be evenly divisible by "4".  In the
              example/ that integer is 12.  Interestingly,
              in every even decade "4" divides evenly
              into the final-digit-2 integer; and in every
              odd decade "4" divides evenly into the
              final-digit-8 integer.  [ Formula for finding
              Decade #: (decade's final-digit-5 integer
              + 5) divided by 10 ]         (285 + 5)/10

Note 1  --- This is where complexity arrives. ---
Example: 280 281 282 283 284 285 286 287 288 289
Odd-integer squares follow this final-digit pattern:  1 9 5 9 1  
as in  1 x 1 = 1, 3 x 3 = 9, 5 x 5 = 25, 7 x 7 = 49, 9 x 9 = 81.
Three ways to find them are: 
1. (a natural number summation sequence term times 8) + 1
2. (an integer times an adjacent integer times 4) + 1
    note: the sum of the two adjacent integers chosen equals the square root
3. (an even integer times an adjacent even integer) + 1
    note: the odd integer between the adjacent even integers is the square root
I'm going to use the latter here.  288/4 = 72  72/2 = 36  36/2 = 18
288/18 = 16      18 - 1 or 16 + 1      17            Also:      
18/2 = 9  72/9 = 8      8 x 9 = 72      8 + 9 = 17
17 is 289's square root.      17 x 17 = 289.
[ sub-note:     5   35   65   95   (x 3)     These are 90-apart locations,
   but 30-apart locations also sometimes contain paired twin primes.
 Both the 30-apart and the 90-apart decades begin at decade 2.
   5 (15/3) is in decade 2 and 95 (285/3) is in decade 29.
   5 x 1 = 5   5 x 7 = 35   5 x 13 = 65   5 x 19 = 95      90-apart
   5 x 1 = 5   5 x 3 = 15  5 x 5 = 25   5 x 7 = 35      30-apart
To get the actual integers/ multiply the products in these
   intentionally-collapsed sequences by "3". ]

Note 2 --  0  4  8   and   2  6  are the two available 
             division-by-4 patterns in each decade

Note 3 --  Regarding the odd squares:  Since the odd squares
             pattern is   1  9  5  9  1   |   1  9  5  9  1, beginning
             at the fifth odd square (81), adjacent occurrences
             of squares having "1" as a final digit/ happen every
             5 squares after 81 and after 121.  Squares having "1"
             as a final digit/ also, starting at 1/ occur every ten odd
             squares (1 x 1 and 19 x 19).  They interlock, however,
             as 19 x 19 is adjacent to 21 x 21.
Integers:   1, 81, 121, 361, 441, 841, 961, 1521, 1681
Decades:   1   9   13    37   45    85   97    153   169
The final-digit-9 squares run:
Integers:   9, 49, 169, 289, 529, 729, 1089, 1369, 1849
Decades:   1   5   17   29    53    73    109   137    185

Note 4 --  final-digit-5 integers evenly divisible by "3"
15   45   75   105   135   165   195   225   255   285   
-
315   345   375   405   435   465   495   525   555   585
-
615   645   675   705   735   765   795   825   855   885
[ sub-note:  The decade pattern for those decades in which "3"
divides evenly into a final-digit-5 integer is:   2  5  8.  
Therefore, only those decades can contain, but may not contain, 
paired twin primes.  One of these decades, 29 (2 + 9 = 11 = 2), 
has 17 x 17 (289) in  it. ]
For the above three rows of integers, the decades are:
2   5   8   11   14   17   20   23   26   29
-
32   35   38   41   44   47   50   53   56   59
-
62   65   68   71   74   77   80   83   86   89

Note 5 --  Whenever "3" divides evenly into a decade, it
also divides evenly into the final-digit-1 integer in that decade.
Some f-d-1 pown squares are in these decades.  One is in 
decade 153:  39 x 39 (1521).  153 digit sums to 9, and so is
not a decade in which "3" divides evenly into its f-d-5 integer.

Note 6 --  More information on decades and "3":
In decade 1, "3" divides evenly into 3 and 6 and 9; and
does the same every third decade from thereon: that is,
it divides evenly into an integer whose final digit is a
3 or 6 or 9.
-
In decade 3, "3" divides evenly into 21 and 24 and 27,
integers whose final digits are 1, 4 and 7 respectively;
and does the same every third decade from thereon.
-
In decade 2, "3" divides evenly into 12 and 15 and 18,
integers whose final digits are 2, 5 and 8 respectively;
and does the same every third decade from thereon.
-
From this it should be obvious why paired twin primes
cannot be found in decades 1, 4, 7, 10, 13, 16, etc.,
or in decades 3, 6, 9, 12, 15, 18, etc.

Note 7 --  Digit addition patterns for integers in decades > 1:
final digit 9:  1 2 3 4 5 6 7 8 9      f-d-1:  2 3 4 5 6 7 8 9 1
f-d-2:  3 4 5 6 7 8 9 1 2      f-d-3:  4 5 6 7 8 9 1 2 3
f-d-4:  5 6 7 8 9 1 2 3 4       f-d-5:  6 7 8 9 1 2 3 4 5
f-d-6:  7 8 9 1 2 3 4 5 6      f-d-7:  8 9 1 2 3 4 5 6 7
f-d-8: 9 1 2 3 4 5 6 7 8      f-d-0:  1 2 3 4 5 6 7 8 9
-
for even squares (if there is a pattern):
4 is 4  16 is 7  36 is 9  64 is 1  100 is 1  144 is 9  196 is 7  
256 is 4  324 is 9   |   400 is 4  484 is 7  576 is 9  676 is 1
784 is 1  900 is 9  1024 is 7  1156 is 4  1296 is 9
4  7  9  1  1  9  7  4  9
-
for odd squares (if there is a pattern):
9 is 9  25 is 7  49 is 4  81 is 9  121 is 4  169 is 7  225 is 9  289 is 1  361 is 1
9  7  4  9  4  7  9  1  1
-
Curious related facts:  17 is 8; 17 x 17 = 289, a 1;  289 is in decade 29, a 2.
39 is 3; 39 x 39 = 1521, a 9; 1521 is in decade 153, a 9.

6:17 PM
Addendum 1:  Began this in Note 3; but moments ago, because I wanted 
to know the changes cycle for odd squares having "1" as a final digit, this:   
1 x 1 = 1      9 x 9 = 81 (9)      11 x 11 = 121 (4)
19 x 19 = 361 (1)      21 x 21 = 441 (9)      29 x 29 = 841 (4)
31 x 31 = 961 (7)      39 x 39 = 1521 (9)      41 x 41 = 1681 (7)
49 x 49 = 2401 (7)      51 x 51 = 2601 (9)      59 x 59 = 3481 (7)
61 x 61 = 3721 (4)      69 x 69 = 4761 (9)      71 x 71 = 5041 (1)
79 x 79 = 6241 (4)      81 x 81 = 6561 (9)      89 x 89 = 7921 (1)
18-term cycle for which the decades are:
1   9   13   37   45   85   |    
97   153   169   241   261   349   |   
373   477   505   625   657   793
Because the final digit for each of these squares is a "1"/
each square/ digit sums to same number its decade does.
This being so, f-d-1 squares do not occur in the decades
where "3" divides evenly into an f-d-5 integer.  Those
decades digit sum to 2, 5 and 8 only.  These decades
digit sum to 1, 4, 7 and 9 only.

Addendum 2:  The f-d-9 squares occur in decades
which digit sum to 1, 2, 5and 8 only, which is why
the 289 square in decade 29 prevents that decade
from containing paired twin primes.
8 PM - This is the 18-term changes cycle for f-d-9 squares:
3 x 3 = 9 (9)    7 x 7 = 49 (4)    13 x 13 = 169 (7)                          1  5  8
17 x 17 = 289 (1)    23 x 23 = 529 (7)    27 x 27 = 729 (9)               2  8  1
33 x 33 = 1089 (9)    37 x 37 = 1369 (1)    43 x 43 = 1849 (4)          1  2  5
47 x 47 = 2209 (4)    53 x 53 = 2809 (1)    57 x 57 = 3249 (9)          5  2  1
63 x 63 = 3969 (9)    67 x 67 = 4489 (7)    73 x 73 = 5329 (1)          1  8  2
77 x 77 = 5929 (7)    83 x 83 = 6889 (4)    87 x 87 = 7569 (9)          8  5  1  


See also:
sw00878math/odd-primes-and-digit-addition
sw00879math/digit-addition-families
sw00881math/pown-and-pewn-squares-notes
sw00882math/descension-by-squares-groups
sw00883math/my-paired-twin-primes-conjecture
sw00884math/more-views-of-my-conjecture  





#
Brian A. J. Salchert

sw00886piks-blossoms

                                         near here

click each to enlarge

Tags: blossoms

sw00885d29--crowded-day-yesterday

 Yesterday began with a necessary fasting after which on a yellow
legal pad I started rough-drafting my heuristically-created paired
twin primes proof for finding them.

About 9:30 my sister arrived to transport me to see a lawyer
regarding important death-related matters.  My sister had an
appointment to see him today, but he provided services for
both of us.  Our experiences with him were brief but pleasant 
and definitely educational.

Then it was on to an outpatient clinic where I was given a not-
so-pleasant (mostly due to my broken nose and broken back
and gag response) esophageal manometry exam.

Next it was north to a supercenter for groceries and other items.

On the way to my apartment we did the Wendy's windows tour 
 for a nearly plain hamburger--their burgers are square and thin
now--for me.  Got to apt around 5:30.

Later I returned to my math project.  Not sure when it will be
finished to my satisfaction.



-
Brian A. J. Salchert    2008-05-13

sw00884math--more-views-of-my-conjecture

30



 Recap:  If "3" doesn't divide evenly into an integer having "2" or "8"
as a final digit, the decade that integer's in does not contain paired
twin primes. 
[ Note: 0 through 9 is the first decade. ]

Continuance:
15      45      75      105      135      165      195      225      255      285
-
Have decided to try this with "3".  12/3 = 4, 18/3 = 6; 42/3 = 14, 48/3 = 16;
72/3 = 24, 78/3 = 26; so on.  5, 15, 25, 35, 45, 55, 65, 75, 85, 95.  If one
multiplies every 30 of these integers by "3", the chance of encountering paired
twin primes is better but not absolute.  Much of this has to do with the integer
squares.  5, 35, 65, 95, and on, are the every 30.  In the first instance, 9 is in
the prior decade and 25 is in the following decade.  In the second instance,
81 is two decades down and 121 is two decades up.  In the third instance,
169 is three decades down and 225 is three decades up.  However, in the
fourth instance, 17 x 17 (289) or (16 x 18) + 1 or (8 x 36) + 1 is in the decade.
Is there anything about the integers from 280 through 289 that signal this? 
1 x 1 = 1, 3 x 3 = 9, 5 x 5 = 25, 7 x 7 = 49, 9 x 9 = 81
11 x 11 = 121, 13 x 13 = 169, 15 x 15 = 225, 17 x 17 = 289, 19 x 19 = 361
Pattern of final digits: 1, 9, 5, 9, 1
49 - 9 = 40 and 289 - 169 = 120.  Beware that pown sqrt whose only or
final digit is "3" or "7".  Am heading higher to see what the spread is there.
21 x 21 = 441, 23 x 23 = 529, 25 x 25 = 625, 27 x 27 = 729, 29 x 29 = 841
169 - 49 = 120 and 529 - 289 = 240.  Internally: 40, 120, 200.

During lunch break, these:
1. The first paired twin primes occur in decade two; and, since every nine
    decades above that decade are the best initial places to look, decades
    11, 20, 29, 38, 47, 56, 65, 74, 83, 92, and so on, are the ones.
2. The following series of integers:
    0 (0 x 1), 2 (1 x 2), 6 (2 x 3), 12 (3 x 4), 20 (4 x 5), 30 (5 x 6), 
    42 (6 x 7), 56 (7 x 8), 72 (8 x 9), 90 (9 x 10), 110 (10 x 11), and on. 
3. If one of these integers is multiplied by "4" and "1" is added to the
    product, the sum will equal an odd square.  72 x 4 = 288; 288 + 1 = 289.
    So 289 is an odd square, but of what?: 8 + 9.
4. 289 exists in the 29th decade.
5. Whatever decade is chosen, it is always wise to divide that decade's
    first integer by "4" and also to divide its ninth integer by "4" to see if
    the remainder is an integer which equals the product of two adjacent
    integers.

Otherconsiderations:
2 x 0 = 0, 2 x 2 = 4, 2 x 4 = 8, 2 x 6 = 12, 2 x 8 = 16, 2 x 10 = 20, 2 x 12 = 24
2 x 6 = 4 x 3    2 x 10 = 4 x 5    2 x 36 = 4 x 18 = 8 x 9 = 72 
-
All the integers in the point 2 example are even integers.  Their pattern is:
0 2 6 2 0
-
In every decade where paired twin primes might be found, both that 
integer whose final digit is "2" and that integer whose final digit is "8"
are evenly divisible by "6".
-
It might be that 288/6 = 48 is an indication 289 is a square since
49 is a square.
-
1 + 8 = 9, 9 + 16 = 25, 25 + 24 = 49, 49 + 32 = 81, 81 + 40 = 121
9 - 3 = 6, 9 + 3 = 12; 25 - 5 = 20, 25 + 5 = 30; 49 - 7 = 42, 49 + 7 = 56
-






#
Brian A. J. Salchert

sw00883math--my-paired-twin-primes-conjecture

29


 Yesterday (Friday, May 09, 2008) I concluded my sw00882math/

descension-by-squares-groups/2841 with this conjecture:  Regarding

paired twin primes, the even integer between one of the twin primes is

always divisible by "4" and the even integer between the other of the

twin primes is always divisible by "6".  Why did I posit this seemingly

senseless conjecture?  Because I wanted to use even integers since I

had set up a descension-by-squares grouping controlled by "4".  As

it happens, the only way my groupings matter is that it was through

them that I uncovered the "4" and "6" phenomenon.  Early this after-

noon, I was trying to find out if I was wrong, an effort which led to:

"3" divides into every six integers, the final digits of which (excluding

the special case: 3 x 3) are 5, 1, 7, 3, 9 as in 15, 21, 27, 33, 39.

Here is a run with the above numbers in italics:

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43

If the final digit is "1" or "7" or "3" or "9", there cannot be any

paired twins primes because 1 + 4 = 5, 7 - 2 = 5, 3 + 2 = 5, 9 - 4 = 5.

Therefore, the final digit must be "5" and the integer must be divisible

by "3".  5 - 3 = 2 and 5 + 3 = 8.  This then is my proof, such as it is.

Also, where the integer whose final digit is "5" is not divisible by "3"/

neither the integer whose final digit is "2" nor the integer whose

final digit is "8" is evenly divisible by "6". 



My effort began with this:

6         102          108          114          120          126          132

4    100     104     108     112     116     120     124     128     132      136

- - -

  99   101   103   105   107   109   111   113   115   117   119   121   123   125   127

   3                  3x5x7                   3             5      3      7      11      3      5



5:01 PM - Have uncovered a flaw.  At the early going it involves "7".  It
is quite obvious, but I failed to check.  "3" divides evenly into an integer
whose final digit is "5" every thirty integers greater than "15" but it isn't
until ninety above "15" that paired twin primes are encountered.  [ This
doesn't invalidate my conjecture as stated, but it certainly weakens it. ]
One obstacle is the odd square.  However, the (8 x an nnss term) + 1
method isn't the only way to find an odd square.  These mulitplications:
2 x 4, 4 x 6, 6 x 8, 8 x 10, 10 x 20, and so on + 1 is another method.
But I had mentioned "7".  Every fourteen from forty-nine it's out to clip
ya, and it doesn't follow an easy-to-detect routine the way "5" and "3"
do.  Perhaps "3" can help, or "5", or both.  Some integers "7" divides
evenly into: one above 55, two below 65, two above 75, one below
85, one above 90, two below 100, at 105, two above 110, one below
120, one above 125, two below 135, at 140, two above 145.  Dizzy
yet?  Which one did I miss?  Correct: at 70.  Routine?  Going back to
7 x 1, the routine begins at two above.  So: two above, one below, one
above, two below, at  |  two above, one below, one above, two below,
at.  I hate "7", which is to say nothing about the greater more difficult
integers.  What about how it relates to mulitiples of "3"?  Which ones?
How about just those that add to 3.  four above 3, two above 12, at 21, 
two below 30, four below 39, three above 39, one above 48, one below 
57, three below 66  |  four above 66, two above 75, at 84, two below
93, four below 102, three above 102, one above 111, one below 120,
three below 129.  All this reminds of a poem I wrote in 2006.  After I
find it I'll place a link to it.  It is 9:35 PM.  Earlier a storm passed.  Need
to see if another one's coming.  Gusts just thrust us.  Satellite's showing
an enlarging green patch over this city.  Dost one blame it on the coal-
fired power plant?  Or is it merely a reflection of the city's lights?  "Bone
Ache" is the poem.  It is the fourth one on its page.  A quick six lines.
It was written September 29, 2006.
It fits this occasion.     





#
Brian A. J. Salchert

sw00882math--descension-by-squares-groups

28


 pewn = positive even whole number      pown = positive odd whole number
 sqrt = square root      resultant = remainder      G = Group      sq = square

 In a descension-by-squares/ pown squares are subtracted from a pewn square
in a lesser to greater order, or pewn squares are subtracted from a pown sq in
a lesser to greater order.  Each subtraction produces a resultant integer which
is always a pown.  That pown is also the product of two integers which can be
discovered by inspecting the sqrt values in a subtraction.  If the values are "18"
and "11", simply subtract the 11 from the 18 to get the multiplier and add the
11 to the 18 to get the multiplicand.  As I will show, the construction of a d-b-s
can quickly become cumbersome, tending to make such constructions less and
less useful.  The main use, however--finding the final resultant, is easily done.
Here are some relevant formulas:
(2 x G#) - 2 = pewn sqrt for that group      G# = (pewn sqrt + 2)/2
(2 x G#) - 1 = pown sqrt for that group      G# = (pown sqrt + 1)/2
(final resultant # + 1)/2 = sqrt      (sqrt x 2) - 1 = final resultant #
Example using the above:
G28      pewn sqrt is 54      final resultant is 107
            pown sqrt is 55      final resutant is 109
[ Note:  Because they are at level one (the x 1 level), some final resultants are
   prime numbers. ]

First ten groups:
-
G1 has one object: 1² - 0² = 1² = 1
-
G2, wherein 2 + 1 = 3 and 3 + 2 = 5:
2 x 2 = 4 _ _ _ _ _ _ _ _ _ _ 3 x 3 = 9
2² - 1² = 3 _ _ _ _ _ _ _ _ _ 3² - 2² = 5
-
G3
4 x 4 = 16 _ _ _ _ _ _ _ _ _ 5 x 5 = 25 
4² - 1² = 15 _ _ _ _ _ _ _ _ 5² - 2² = 21
4² - 3² = 7 _ _ _ _ _ _ _ _ _5² - 4² = 9
-
G4
6 x 6 = 36 _ _ _ _ _ _ _ _ _ 7 x 7 = 49
6² - 1² = 35 _ _ _ _ _ _ _ _7² - 2² = 45
6² - 3² = 27 _ _ _ _ _ _ _ _7² - 4² = 33
6² - 5² = 11 _ _ _ _ _ _ _ _7² - 6² = 13
-
G5
8 x 8 = 64 _ _ _ _ _ _ _ _  9 x 9 = 81
8² - 1² = 63 _ _ _ _ _ _ _ 9² - 2² = 77
8² - 3² = 55 _ _ _ _ _ _ _ 9² - 4² = 65
8² - 5² = 39 _ _ _ _ _ _ _ 9² - 6² = 45
8² - 7² = 15 _ _ _ _ _ _ _ 9² - 8² = 17
-
G6
10 x 10 = 100 _ _ _ _ _ _ 11 x 11 = 121
10² - 1² = 99 _ _ _ _ _ _ 11² - 2² = 117
10² - 3² = 91 _ _ _ _ _ _ 11² - 4² = 105
10² - 5² = 75 _ _ _ _ _ _ 11² - 6² = 85 
10² - 7² = 51 _ _ _ _ _ _ 11² - 8² =57
10² - 9² = 19 _ _ _ _ _ _ 11² - 10² = 21
-
G7
12 x 12 = 144 _ _ _ _ _ _13 x 13 = 169
12² - 1² = 143 _ _ _ _ _ 13² - 2² = 165
12² - 3² = 135 _ _ _ _ _ 13² - 4² = 149
12² - 5² = 119 _ _ _ _ _ 13² - 6² = 129
12² - 7² = 95 _ _ _ _ __13² - 8² = 105
12² - 9² = 63 _ _ _ _ _ _13² - 10² = 69
12² - 11² = 23 _ _ _ _ _ 13² - 12² = 25
-
G8
14 x 14 = 196 _ _ _ _ _ _ 15 x 15 = 225 
14² - 1² = 195 _ _ _ _ _ _15² - 2² = 221
14² - 3² = 187 _ _ _ _ _ _15² - 4² = 209
14² - 5² = 171 _ _ _ _ _ _15² - 6² = 189
14² - 7² = 147 _ _ _ _ _ _15² - 8² = 161
14² - 9² = 115 _ _ _ _ _ _15² - 10² = 125
14² - 11² = 75 _ _ _ _ _ _15² - 12² = 81
14² - 13² = 27 _ _ _ _ _ _15² - 14² = 29
-
G9
16 x 16 = 256 _ _ _ _ _ _ 17 x 17 = 289
16² - 1² = 255 _ _ _ _ _ _17² - 2² = 285
16² - 3² = 247 _ _ _ _ _ _17² - 4² = 273
16² - 5² = 231 _ _ _ _ _ _17² - 6² = 253
16² - 7² = 207 _ _ _ _ _ _17² - 8² = 225
16² - 9² = 175 _ _ _ _ _ _17² - 10² = 189
16² - 11² = 135 _ _ _ _ _ 17² - 12² = 145
16² - 13² = 87 _ _ _ _ _ _17² - 14² = 93
16² - 15² = 31 _ _ _ _ _ _17² - 16² = 33
-
G10
18 x 18 = 324 _ _ _ _ _ _ 19 x 19 = 361
18² - 1² = 323 _ _ _ _ _ _19² - 2² = 357
18² - 3² = 315 _ _ _ _ _ _19² - 4² = 345
18² - 5² = 299 _ _ _ _ _ _19² - 6² = 325
18² - 7² = 275 _ _ _ _ _ _19² - 8² = 297
18² - 9² = 243 _ _ _ _ _ _19² - 10² = 261
18² -11² = 203 _ _ _ _ _ _19² - 12² = 217
18² - 13² = 155 _ _ _ _ _ 19² - 14² = 165 
18² - 15² = 99 _ _ _ _ _ _19² - 16² = 105
18² - 17² = 35 _ _ _ _ _ _19² - 18² = 37

[ Note: I was surprised when 4 and 28 had prime pairs which do not match
   when digit addition is applied to them, but have since learned that there 
   are congruities in two other ways.  28 - 4 = 24, which is divisible by both
   3 and 8; 107 - 11 = 96, which is divisible by both 3 and 8. ]

Guess what.  Unless I've made an error someplace, I've just been thrown
another dropping curve ball I cannot hit.  191, 193; 197, 199 are primes.  
G49      pewn sqrt is 96      final resultant is 191
            pown sqrt is 97      final resultant is 193

Plainly put, if the even integer between two primes is not
divisible by "4", those primes will not be in the same group.

[ Note:  What I have been calling prime pairs are usually
   called twin primes; so I guess one could call 11 13 and
   17 19 paired twin primes.  In every such pairing, only
   the even integer between one of the twins is divisible by
   "4".  Not sure, but the integer between the twin primes
   which is not divisible by "4" may always be divisible by
   "6". ]

9:27 PM - With help from a table on page 211 of the paperback
copy of The Mathematical Experience I own, just discovered
that 9431 9433 and 9437 9439 are paired twin primes, and that
9432 is divisible by "4" and 9438 is divisible by "6".

Conjecture:  Regarding paired twin primes, the even integer 
between one of the twin primes is always divisible by "4"
and the even integer between the other of the twin primes   
is always divisible by "6". 




#
Brian A. J. Salchert

sw00881math--pown-and-pewn-squares-notes

27


 pown = positive odd whole number         da = digit addition
 sq = square         tpo = term position         DF = descension family
 pewn = positive even whole number        sqrt = square root

There are no integer squares in the 2, 3, 5, 6, 8 da families.
[ The even squares run: 4 7 9 1 1 9 7 4 9 ]
The sq of any pown/ divisible by "3" is in the 9da family.

tpo          pown          sq          da
-
 1              1               1           1
 2              3               9           9
 3              5              25          7
 4              7              49          4
 5              9              81          9
 6             11            121          4
 7             13            169          7
 8             15            225          9
 9             17            289          1

The da family rotation above is Group 1.  19 through 35 comprises Group 2.
Here is a different view:

pown          1          3          5          7          9          11          13         15         17
-
sq da          1          9          7          4          9           4           7           9           1
--
pown         19        21        23         25         27         29          31         33         35
-
pown         37        39        41         43         45         47          49         51         53

The goal I have may have already been reached, and it may be I cannot reach it;
but that is neither here nor there, and at this moment I am reluctant to reveal it.
-
In the 1da family for pown squares, the powns are separated from each other
in a 16 2 pattern.  In the 4da family for pown squares, the pattern is 4 14; and
in the 7da family for pown squares, the pattern is 8 10.  In each case, 18 apart
rules when going from a given column in one group to the same column in the
group above or below it.
-
Also, there is a times-10 rule helper.  Example:  49 + (7 x 10) = 119 (or 7 x 17).
This is leading to final-digit math regarding both pown and pewn squares.  I may
need to change the title of this entry.  Anyway, here's the info:
Am skipping "1".  Am skipping "5".  9 + (3 x 10) = 39 (or 3 x 13),
121 + (11 x 10) = 231 (or 11 x 21); 361 + (19 x 10) = 551 (or 19 x 29).
So, where the final digit is "9" in the above, a 120 - 1 and a 40 -1 occur.
Where, likewise, the final digit is "1", a 230 + 1 and a 550 + 1 occur.
Similar outcomes occur with pewn squares.  4 + (2 x 10) = 24 (or 2 x 12)
and 64 + (8 x 10) = 144(or 8 x 18).  16 + (4 x 10) = 56 (or 4 x 14) and
36 + (6 x 10) = 96 (or 6 x 16).  So, where the final digit is "4", a 25 - 1 and
a 65 - 1 occur.  Where the final digit is "6", a 55 + 1 and a 95 + 1 occur.
Obviously, pown squares revolve around "0" and pewn squares revolve
around "5". 

May 08, 2008
Late last night before I lost my broadband connection, I subtracted
119 from 144.  The 25 reminded me of descension-by-squares and
Descension Families.  Visit this entry.  Moments ago I was there and
I think it is better than what I had planned to write here.  Still, I never
know when a rethinking will move me to change terminology and/or how 
an idea is presented.  For instance: there I let 3² - 2² be a DF of one
level; but it could be a DF of two levels.  The former is as above/
where the resultant integer is "5".  Were I to show it as two levels,
the second level would be 3 x 3 = 9, and would be there mainly for
informational reasons.  "5" would still be the resultant integer, the
final resultant integer, that is.

Do want to add some further thoughts.
-
It could be said that "3" and "5" are the only two-level (or one-level) DF
primes.  . . .  After the 8DF (4 x 4 = 16) comes the 10DF (5 x 5 = 25).
[ Haven't done an extensive check, but it appears the DF's rise in pairs.
If so, they could be grouped so, and this might aid in understanding the
secrets of the final resultants.  Will probably be heading that direction. ] 
Proceeding with my changed thinking, these are the only three-level DF's,
and the final resultant for the 10DF is not a prime.  Here is the new look:
5 x 5 = 25
5² - 2² = 21
5² - 4² = 9 = 3²
Points of interest: 
5² descends to 3², 13² to 5², 25² to 7², 41² to 9²,
61² to 11², 85² to 13², 113² to 15²; 145² to 17².
This generates the following:
8        12        16        20        24        28        32
For going beyond 113² there is this, in which multiples of "36" reign:
5²     41²     113²     221²     365²     545²     761²
These are for descensions to squares which are multiples of "3".
The resulting squares are:  9, 81, 225, 441, 729, 1089; 1521.
Here:  761² - 760² = 1521 = 39 x 39.    



#
Brian A. J. Salchert

sw00880d28--read-my-blogs-if-but

   you are also welcome to use this one and my 
bajsalchert.blogspot.com one as gateways to
other web logs.  Here in the Favorite Places
sidebar section are links to a variety of sites.
Take a look.  The one I visit the most is the
Astronomy site, but a site such as the HTML
ASCII site (www.lookuptables.com) often
helps when I need to know special codes.

My blogspot blog has more links to sites
maintained by other writers (mostly poets).
Its name is Rhodingeedaddee.



Brian A. J. Salchert    2008-05-07

sw00879math--digit-addition-families

26


 Confusion reigns even where there is order.


1, 10, 19, 28, 37, 46, 55, 64, 73, 82   |   91, 100, 109, 118, 127, 136, 145, 154, 163, 172
-
2, 11, 20, 29, 38, 47, 56, 65, 74, 83   |   92, 101, 110, 119, 128, 137, 146, 155, 164, 173
-
3, 12, 21, 30, 39, 48, 57, 66, 75, 84   |   93, 102, 111, 120, 129, 138, 147, 156, 165, 174
-
4, 13, 22, 31, 40, 49, 58, 67, 76, 85   |   94, 103, 112, 121, 130, 139, 148, 157, 166, 175
-
5, 14, 23, 32, 41, 50, 59, 68, 77, 86   |   95, 104, 113, 122, 131, 140, 149, 158, 167, 176
-
6, 15, 24, 33, 42, 51, 60, 69, 78, 87   |   96, 105, 114, 123, 132, 141, 150, 159, 168, 177
-
7, 16, 25, 34, 43, 52, 61, 70, 79, 88   |   97, 106, 115, 124, 133, 142, 151, 160, 169, 178
-
8, 17, 26, 35, 44, 53, 62, 71, 80, 89   |   98, 107, 116, 125, 134, 143, 152, 161, 170, 179
-
9, 18, 27, 36, 45, 54, 63, 72, 81, 90   |   99, 108, 117, 126, 135, 144, 153, 162, 171, 180


#

First:  There cannot be a "0" digit-addition (0da) family.
Second:  In the 9da there is no prime number.
Third:  Each single-digit prime is also the da it is in (2, 3, 5, 7).
Fourth:  The first prime in the 1da is "19".
Fifth:  In the 6da there is no prime number.
Sixth:  The first prime in the 4da is "13".
Seventh:  The first prime in the 8da is "17".
Eighth:  In the 3da the only prime is "3".
Ninth:  Every integer in the 3da, 6da, and 9da is divisible by "3".
Tenth:  Each digit-addition family has a 10-term pattern.
Eleventh:  There are only 9 da patterns 
                   pertaining to powns and their pown multiples,
                   and each of these patterns has 9 terms,
                   and "9" is the 5th term in each pattern.  
                   Why?  The da pattern repeats after every 9 terms
                   because the da for x 1 equals the da for x 19; and,
                   for this same reason, the da pattern repeats after
                   every 18th higher pown.  19's da and 37's da is "1".
                   Also, any integer times 9 equals a 9da integer.

How crazy I am is an unknown; nonetheless, I'm pressing on.

One interest is knowing how a prime relates to its square.  Did a few
calculations and it seems that in a given da family, both the primes and
the squares of those primes, while each in a different da family, are
respectively in the same da family.  Thus, if the prime is in the 1da, its-- 
this is an exception--square is inthe 1da.  
If a prime is in the 2da, its squareis in the 4da.
If a prime is in the 3da (and only one is), its square is in the 9da.  
If a prime is in the 4da, its square is in the 7da (because 4 x 4 = 16).
If a prime is in the 5da, its square is in the 7da (because 5 x 5 = 25).
If a prime is in the 7da, its square is in the 4da.
If a prime is in the 8da, its square is in the 1da.

So?  Sew baritones on your underwear.

Now, 11 (2da) times 17 (8da) equals 187 (7da)
and 29 (2da) times 53 (8da) equals 1537 (7da).
-
What about 105, which is 3 x 5 x 7?
-
This is heading into combinatorics.
-
29 (2da) times 19 (1da) equals 551 (2da),
and 11 times 37 equals 407.
29 times 13 equals 377 (8da).
29 times 23 equals 667 (1da).
29 times 43 equals 1247 (5da).
29 times 47 equals 1363 (4da).
-
Conclusion 1:  Every integer product is divisible by "1".
Conclusion 2:  The da of a pown product may be divisible by a pown
                        of any other da.

Had to fix an error in the da chart.  After the correction, I noticed that "11"
and "101" are both 2da, that "13" and "103" are both 4da, that "17" and
"107" are both 8da, and that "19" and "109" are both 1da.  This suggests
that at multiples of 90 there may be other such prime pairs.  In order to
avoid being misunderstood, the pairs here are 11 and 13, 17 and 19,
101 and 103, 107 and 109.  90 up from 105 is 195 (3 x 5 x 13), and
neither 7 nor 11 divide without remainders into 191, 193, 197, or 199.
A prime does not assert its power until it attains its square.  Primes > 13
do not, therefore, matter.  17 x 17 = 289. 






#
Brian A. J. Salchert

sw00878math--odd-primes-and-digit-addition

25


 Have off-and-on been trying for years to find a way to know
by inspecting it if an integer is divisible by a prime number.  It
is easy to tell if it is divisible by "5", and only slightly harder 
to tell if it is divisible by "3"; but from "7" on up it is difficult.
Tonight I decided to try numerological digit addition, and may
have uncovered a way.

digit addition = da          times = x

patterns:
-
3
3     9     6     3     9     6     3     9     6               da
1     3     5     7     9    11    13   15    17               x
5
5     6     7     8     9     1     2     3     4               da
1     3     5     7     9    11    13   15    17               x
7
7     3     8     4     9     5     1     6     2               da
1     3     5     7     9    11    13   15    17               x
11
2     6     1     5     9     4     8     3     7               da
1     3     5     7     9    11    13   15    17               x
13
4     3     2     1     9     8     7     6     5               da
1     3     5     7     9    11    13   15    17               x 
17
8     6     4     2     9     7     5     3     1               da
1     3     5     7     9    11    13   15    17               x
19
1     3     5     7     9     2     4     6     8               da
1     3     5     7     9    11    13   15    17               x
23
5     6     7     8     9     1     2     3     4               da
1     3     5     7     9    11    13   15    17               x
29
2     6     1     5     9     4     8     3     7               da
1     3     5     7     9    11    13   15    17               x
-
Interesting.  There are 9 terms in each rotation.
The greatest multiplier in each rotation is 18 less than
the greatest multiplier in the next higher rotation.  Every
prime which is 18 greater than a lesser prime has the
same digit-addition rotation as the lesser prime.  This
means there are da-rotation families.  However, it   
would be better to use a prime's da.  Example: 11's 
da is 2, 29's da is 2, 47's da is 2, but 65 is not a prime.
-
Will need to continue this another day.  




#
Brian A. J. Salchert

sw00877math--1-3-5-7-9

 Certain groups with 5 terms.  Not sure where this will go.

1 3 5 7 9   3 9 15 21 27   5 15 25 35 45   7 21 35 49 63   9 27 45 63 81

Two times in the above is the only odd integer prime triad: 3 5 7

11 33 55 77 99   13 39 65 91 117   15 45 75 105 135   17 51 85 119 153
       19 57 95 133 171   21 63 105 147 189   23 69 115 161 207

Not much to behold.   11 13  17 19  23

So what is of interest?  x 1  x 3  x 5  x 7  x 9

The first integer in each group gets the group name, but not the gpo.
A group's position is always its (first integer + 1)/2.  Thus, the gpo
of the 23 Group is 12.  It happens that "23" is a prime number and
that therefore 24 (3 x 8) - 1 equals a prime number.  So what?  I
am not certain, but (1 x 8) - 1 equals a prime number too.  What
other single-digit integers work?  (9 x 8) - 1, but neither (5 x 8) - 1
nor (7 x 8) - 1.  (2 x 8) - 1?  No.  (4 x 8) - 1?  Yes.  (6 x 8) - 1?
Yes.  (8 x 8) - 1?  No.  Messy.  Yet maybe not.  The "Yes" ones
are: 7, 23, 31, 47, 71.  The "No" ones are: 15, 39, 55, 63.  It
appears that multiples of "3" matter extensively.

Something else.  The what's missing game.  This involves powns only
after 3 5 7, and forget integers that have "5" for a final digit.  In the 3
Group the missing powns are 11, 13, 17, 19, 23.  Beyond this group
the search toughens/ because some of the missing integers show up in
higher groups.  My interest in this method is weakening.

Something other.  The spreads, and where they occur.  Of course, a
higher strangeness exists in the higher realms, so I may not get far here
either.  3 [2] 5 [2] 7 [4] 11 [2] 13 [4] 17 [2] 19 [4] 23 [6] 29 [2] 31 [6]
37 [4] 41 [2] 43 [4] 47 [6] 53 [6] 59 [2] 61 [6] 67 [4] 71 [2] 73 [6] 79
[4] 83 [6] 89 [8] 97 [4] 101 [2] 103 [4] 107 [2] 109 [4] 113 [14] 127 
Notice that before we encounter the two prime pairs above 100 we hit
the first 8-apart, and after 113 we hit a stunning 14-apart dead zone.
What's with 115, 117, 119 121, 123, 125?  5, 3, 7, 11, 3, 5.  "119",
being two less than an odd square, should be (according to previous
experiences) a prime number, but 7 x 17 invalidates that assumption.
The immediate realization is that more of the same can be expected. 

083
085   5 x 17
087   3 x 29
089
091   7 x 13
093   3 x 31
095   5 x 19
097
099   3 x 3 x 11
101   
103
105   3 x 5 x 7   (105 is a major node integer)
107
109
111   3 x 37
113
115   5 x 23
117   3 x 3 x 13
119   7 x 17
121   11 x 11
123   3 x 41
125   5 x 5 x 5
127





#
Brian A. J. Salchert

sw00876i--listeria-info

meat recall and general information about listeria

sw00875math--even-squares-to-odd-squares

  This is another revisit to the natural number summation sequence
and its relation to "8".

Excluding "0", the first twelve nnss terms are: 
1 3, 6 10, 15 21, 28 36, 45 55, 66 78

   These can be approached variously; but how even squares are
progenitors of them, and how odd squares are derived from them
is valuable knowledge.

As can be seen, this sequence can be shown in 2-term groups
because the first two are odd integers and the second two are
even integers, and so on in that alternating manner.

Things to note:
1 + 3 = 4; 6 + 10 = 16; 15 + 21 = 36; 45 + 55 = 100; and
so on in that manner.  Obviously, the sums are even squares,
meaning that hidden in any even square are two terms of the
natural number summation sequence.  Therefore, if 12 x 12
(or 144), is chosen for inspection, how are the nnss terms
in it exposed?  If 144 is divided by 2, the quotient is 72.  If
12 is divided by 2, the quotient is 6.  72 - 6 = 66, and 72
+ 6 = 78.  As per above, 66 and 78 constitute a group of
two even terms in the natural number summation sequence
(nnss).
-
How do odd squares relate to this?  Every odd square is
1 > any nnss term (including "0") multiplied by "8".  So,
say the target is 13 x 13 (or 169).  How is it discovered?
One way is to subtract "1" from "169" and then divide
"168" by "8".  Having done this, the next question is: 
What is the proof that "21" is an nnss term?  There are
several ways, but I want to try something.  In the nnss
there are odd groups and even groups.  Since the first
group is an odd group, I'm calling the odd groups the
minor sequence, making the even groups the major
sequence.  Now 1 + 3 = 4, so "4" is a number which
can be used as a divisor.  Here's a run:
.25, .75; 3.75, 5.25; 11.25, 13.75; 22.75, 26.25
Here's a run using even nnss terms:
1.5, 2.5; 7, 9; 16.5, 19.5; 28, 36
I'm sure you see the difference and also the nuances.
4 into 21 = 5.25, but--.  .25 represents "1"; therefore,
if 5.25 is divided by .25, the quotient should be 21,
and it is.  "21" is the sixth term in the nnss, which means
that it is the sum of 1 + 2 + 3 + 4 + 5 + 6.  If term position
(tpo) is used as a guide, the results of dividing each term by
its position creates an incontrovertible sequence:
1, 1.5, 2, 2.5, 3, 3.5, n
Each of these numbers can also be obtained by adding "1"
to an nnss tpo and then dividing by 2.  From this it is also
possible to get back to an nnss term's value by subtracting
.5 from the (tpo + 1)/2 quotient and then multiplying that 
by the (tpo + 1).  3.5 - .5 = 3, and 3 x 7 = 21.
[ By these methods any unknown nnss term can be found.
   Example:  Let 63 be the tpo for an nnss term.  63 + 1 = 64.
   64/2 = 32.  64 x 31.5 = 2016. ]  So sayeth my calculator.
What then is this?: (8 x 2016) + 1.  16129.  What is the sqrt
of that?  Three calculator tries got me "127".
-
3² 5²   7² 9²   11² 13²   15² 17²   19² 21²   23² 25²
Now, the square root (sqrt) 
of 4 is 2; of 16 is 4; of 36 is 6; of 64 is 8; of 100 is 10; of 144 is 12
and
2 x 2 = 4, 2 x 4 = 8, 2 x 6 = 12, 2 x 8 = 16, 2 x 10 = 20; 2 x 12 = 24
Remember
1 + 3 = 4, 6 + 10 = 16, 15 + 21 = 36, 28 + 36 = 64, 45 + 55 = 100; 66 + 78 = 144
and
4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, 4 x 4 = 16, 4 x 5 = 20; 4 x 6 = 24
So, if the 2-term group position is 32, the integer between the odd square roots
 of each term in that group must be 4 x 32, which is 128.  See "127" above.
If the spread between the nnss terms in a group is known,
 then that value divided by 2 will equal that group's position (gpo). 
Therefore, (32 x 2) + 2016 must equal a term whose value is 2080;
 and (8 x 2080) + 1 must equal an odd integer which is 129 x 129.
 According to my calculator/ both the former and the latter is 16641.
Of course, then, the difference between the odd squares 
 divided by the spread between the related nnss terms
 will always equal "8".  




#
Brian A. J. Salchert

sw00874math-3at4

22


 There are two ways three adjacent integers can be related to "4"
that are of interest to me.  The one way I am not choosing first
begins at zero.  In the 6n Elimination Table the odd squares
always occur in the +1 column, the column beginning with "7".
In today's entry, "4" controls the distribution, but the first n is "1",
and each n is a pown integer which is 2 > the preceding n, and "2"
is the multiplier, and the odd squares always occur in the -1 column,  
 and there is only one row.
#

1 2 3   5 6 7   9 10 11   13 14 15   17 18 19   21 22 23   25 26 27

29 30 31   33 34 35   37 38 39   41 42 43   45 46 47   49 50 51

53 54 55   57 58 59   61 62 63   65 66 67   69 70 71   73 74 75

77 78 79   81 82 83   85 86 87   89 90 91   93 94 95   97 98 99

101 102 103   105 106 107   109 110 111   113 114 115   117 118 119

121 122 123   125 126 127   129 130 131   133 134 135   137 138 139

141 142 143   145 146 147   149 150 151   153 154 155   157 158 159

-
final-digit rotations:  1 5 9 3 7; 2 6 0 4 8; 3 7 1 5 9

Since this row consists of groups of three adjacent integers,
the first group having a prime pair is:  5 6 7

Beginning with 5 6 7, every group which is greater by "12"
than the group preceding it/ might--except for those groups
in which "4" or "6" is the final digit--contain a prime pair.
The final-digit rotation is: 6 8 0 2 4.              

Here are the first four:  5 6 7   17 18 19   29 30 31   41 42 43

Beginning with 53 54 55, problems:  65 66 67   77 78 79   89 90 91
do not contain prime pairs because of "5" in the first two, and of "7"
in the second two.  In both cases "11" and "13" are the complicit
multiplicands.

Then comes 101 102 103, wherein 101 and 103 is a prime pair.

Then comes 137 138 139, wherein 137 and 139 is a prime pair.

Then comes 149 150 151, wherein 149 and 151 is a prime pair.

Then comes 161 162 163, but/ 7 x 23 = 161.
Notice: 23 - 11 = 12; 25 - 13 = 12.  Okay, backtrack.
5 x 23 = 115   5 x 25 = 125   7 x 23 = 161   7 x 25 = 175

Further:  175 - 70 = 105; and 175 - 14 = 161, and 105 - 14 = 91
Also:  105 + 14 = 119, and 175 + 14 = 189
So these:  3 x 7, 5 x 7, 7 x 7; 13 x 7, 15 x 7, 17 x 7; 23 x 7, 25 x 7, 27 x 7
[ This means that "5" controls distribution--downwards and upwards--
for every pown including itself via a 1 x, 3 x, 5 x, 7 x, 9 x rotation of
single digits and final digits. ]
The node number "105" is a good small example of this/ because it
isdivisible by 3 and 5 and 7, forcing "3" to 102 and 108; forcing "7"
to 98 and 112; and thereby allowing 101, 103, 107, and 109 to be
prime numbers.

-
"107" and "109" bring me to the second way, which I will begin
at "4" instead of at "0".  The rotation is: 4 8 2 6 0

3 4 5   7 8 9   11 12 13   15 16 17   19 20 21   23 24 25   27 28 29

31 32 33   35 36 37   39 40 41   43 44 45   47 48 49   51 52 53   55 56 57

59 60 61   63 64 65   67 68 69   71 72 73   75 76 77   79 80 81   83 84 85

87 88 89   91 92 93   95 96 97   99 100 101   103 104 105   107 108 109

111 112 113   115 116 117   119 120 121   123 124 125   127 128 129

131 132 133   135 136 137   139 140 141   143 144 145   147 148 149

151 152 153   155 156 157   159 160 161   163 164 165   167 168 169

In this view the pown squares always occur in the +1 column.

After 3 4 5, wherever a "4" or a "6" is a final digit in a group, the powns
in it cannot be a prime pair.

Beginning with 11 12 13, it appears that only where the pewn of a group
is divisible by "12" can its powns possibly be a prime pair.  In this view
it also appears there are fewer prime pairs.

In the first view the first prime pair is in the 5 6 7 group.  "6" is 6 x 1.
In this view "12" is 6 x 2.  I am deducing from this that in the first
view the pewn in a group containing a prime pair will always be an
odd multiple of "6", whereas in the second view the pewn in a group
containing a prime pair will always be an even multiple of "6". 






#
Brian A. J. Salchert

sw00873d27

  Anomaly

 In God we trust;
 in Satan we thrust.





Brian A. J. Salchert    2008-05-01

sw00872ut-38.2poems

The Undulant Trees



 Opportunity

I had a life once, a life/
handed to me on a golden matter:
more, more, & more; but
did not see it, and let it pass.




 April's End


'Tis the last day of April.
'Tis, 'tis, 'tis.                  
Oh how quickly 30 whizz.

And here I sit,
sullen and somber,
where undulant evil is.

Yo, rise/ from your stool.
There are reams to conquer,
twirling fool.




-
Brian A. J. Salchert

sw00871d26-melodies

 Lately melodies have been streaming through my body
in strings that go on for an hour or more.  It got so tonight
that I felt I was getting to be like (ha ha) Franz Schubert.
This led to a Franz Schubert search and to Wikipedia.   
That man, sometimes known as the little mushroom, was
amazing!  He wrote over 600 lieder, a fact alone, given
that he died at the age of 31, enough to assure his fame;
but he also composed chamber music, operas, and was
working on (I believe) his 10th symphony when he died.

These melodies in me come out as modulated exhalings.
I need to get some recording equipment.  It could be
that these melodies already exist and I am just pulling
them out of the ether somehow.  Sometimes, as now,
I'll get stuck on one and repeat it over and over.  At
other times one or two notes in one melody will lead
me into another melody, one which may or not/ be
related to the progenitor melody.  It's strange, but it
can be enjoyable.

Years ago there was a period when I was composing
parts of symphonies in a similar manner, but I was not
able to transcribe them.  I still am not able to, and the
only instrument I can play is my breath instrument. 



Brian A. J. Salchert    2008-04-28

sw00870math-3zs5zs7zs.part2

 Other integer knowns pertaining to primes and nonprimes:
-
1.  What I call Elimination Tables can be constructed/ wherein
    2 x the pown (positive odd whole number) whose mulitples
    are being eliminated generates the first pewn divisible by 
    that pown.  That pewn and the integer multiples of it become 
    C2 of a three-column table/ wherein C1 contains all the 
    powns which are 1 less than each C2 pewn, and C3 contains  
    all the powns which are 1 greater than each C2 pewn.  If "3"
    and its multiples are the powns being eliminated, all the powns
    not divisble by "3" will be among the minor or major powns 
    in the table.  Many of these powns will be prime numbers, but
    note that all the squares of powns will be major powns.
2.  Some facts about squares, powns, and pewns:
    a) Subtracting 1 from any pewn square whose final digit is 6
        equals a pown which is divisible by "5".
    b) Subtracting 2 from any pown square often equals a pown
        which is a prime number, but there are some interesting
        exceptions.  119, or 7 x 17, is one of these.
    c) The recurring final-digit sequence for pewn squares is:
        4, 6, 6, 4, 0; and
        the recurring final-digit sequence for pown squares is:
        1, 9, 5, 9, 1.
    d) The Elimination Table for multiples of "3" is the 6n table.
        At each 6n (C2), the C1 pown and the C3 pown
        constitute a pair such as 5 7, 11 13, 17 19, 23 25, 29 31,
        35 37, 41 43, 47 49, 53 55, 59 61, 65 67, 71 73, 77 79,
        83 85, 89 91, 95 97, 101 103, 107 109, 113 115, 119 121.
        If this table is taken into infinity, all the possible prime pairs
        exist in it.
    e) Any integer whose final digit is 5, being divisible by "5", is
        automatically a nonprime.  Therefore, for all powns > 9
        only those powns whose final digits are 1 or 3 or 7 or 9
        need be inspected for primality.
    f) 2 is the only pewn prime, and the only pown prime triad is:
        3 5 7.
    g) An integer's power begins at its square.  This is why "2"
        is the only pewn prime.  This is also why the lesser of
        two pown integers is always the ruling eliminator of 
        integers greater than itself. 



Brian A. J. Salchert

sw00869math-3zs5zs7zs

(  3)   1+2     4+5      7+8     10+11    13+14    16+17    19+20    22+23

(  5)   2+3     7+8     12+13    17+18    22+23    27+28    32+33    37+38

(  7)   3+4    10+11    17+18    24+25    31+32    38+39    45+46    52+53

(  9)   4+5    13+14    22+23    31+32    40+41    49+50    58+59    67+68

( 11)   5+6    16+17    27+28    38+39    49+50    60+61    71+72    82+83

( 13)   6+7    19+20    32+33    45+46    58+59    71+72    84+85    97+98

( 15)   7+8    22+23    37+38    52+53    67+68    82+83    97+98   112+113

#
About 1+2, 2+3, 3+4, and:  The first # = the row #,
and the second # indicates the column # where the square of the ( #) is.
#
Next: If the two adjacent #s which sum to a ( #) exists in a prior row,
that ( #) is not a prime #.  Example: 4+5 is in row 1 column 2, and
4+5 is also in row 4 column 1.
#
Next:  Column 1 is the x1 column, C2 is the x3 column, C3 the x5,
C4 the x7, C5 the x9, C6 the x11, C7 the x13; C8 the x15.  So,
(column # x2) - 1 = the times # for that column.
#
Next:  Since 4+5 is in C2 of R1, which is 3s row, 4+5 = 3x3.
#
Next:  That # which is the second # in R1C1 is the first in R2C1.
This means that there are three distinct numbers C1 of any two
adjacent rows.  These three #s in C1 of R1 and R2 sum to 6.
These three #s in C1 of R2 and R3 sum to 9.  These three #s
in R5 and R6 sum to 18, or 3x6.  The ( #) in R5 is 11, and the
( #) in R6 is 13.  11+13=24, or 3x8.  24 - 18 = 6.  Go back.
3+5=8; 8 - 6 = 2.  5+7=12; 12 - 9 = 3.  So, the distinct #s in
adjacent rows rise by 3, and ( #)s in adjacent rows rise by 4 
when they are summed as terms in a set of adjacent rows.  I
am not yet certain what the value of knowing these facts is,
but I suspect there is an interpolation value.  
#
Next:  A known about primes is that there is a prime number
between n and 2n for every integer n > 1.
If n = 2, 2n = 4.  3 is between 2 and 4.  If n
= 3, 2n = 6.  5 is between 3 and 6.  If n = 4,
2n = 8.  Both 5 and 7 are between 4 and 8.  If n
= 5, 2n = 10.  Both 7 and 9 are between 5 and 10, but
we know that 9, or (10 - 1),  is not a prime.  Between 8 and 16
are 9, 11, 13, and 15.  Question:  Why do 5+6 and 6+7 equal
numbers which are prime numbers, while 4+5 and 7+8 do not? 



Brian A. J. Salchert

sw00868d25

 Yesterday I joined Goodreads, a free connectivity service
for people who read.

 Anyone interested in a recipe for a large batch
of really hot chili should go to my Other Journals
section and click on      a place in Ohio.
-                                                 
[ 2008-10-23 note: the place in Ohio is in limbo
   and I'm not sure when it will return from there,
   if it does return. ]



Brian A. J. Salchert    2008-04-23

sw00867d24

Earth Day 2008

sw00866d23

d = diddlings


     Do not particularly like this Verdana size 3,
but I tried Times New Roman and Courier New
and did not like them.  I had a wrong impression
about the former and, as I have known, the latter
is like typewriter type--which I like--but is too light.
The jump from 2 to 3 in Verdana is too great.  I
would prefer a size between those choices.


This is Verdana size 2.


This is Georgia size 3.
a b c d e f g h i j k l m n o p q r s t u v w x y z 0 1 2 3 4 5 6 7 8 9
-
Though it's a bit heavy, I may go to this.


This is Trebuchet MS size 3.
a b c d e f g h i j k l m n o p q r s t u v w x y z


This is Courier New size 4.


This is Perpetua size 5.
a b c d e f g h i j k l m n o p q r s t u v w x y z

-
-

Should get back to entering my old online diaries
but I just don't feel up to it.  Keep floating around
the Internet for other web logs of interest to me.
Have found several.

Spring has sprang, and I took some photos over
the weekend of things in bloom and of bushes
displaying variant colors.  Today it warmed up
enough for me to go to my mailbox without a
jacket.

-
-

An interesting serendipity occurred this evening
which relates to a poem by Sir Thomas Wyatt.

Read what Boyd Tonkin writes about himself 
in his "Why poetry still matters" feature


and then go K. Silem Mohammad's site where
he shows and discusses the same poem.

see Monday, April 14, 2008




Brian A. J. Salchert    2008-04-21

sw00865d22

d = design


two articles from Technology Review

"Nano Drugs to Starve Tumors"
By Jocelyn Rice - Friday April 11, 2008
(about fighting cancer more safely)

"Corn Primed for Making Biofuel"
By Alexandra M. Goho - Wednesday April 16, 2008
(about less expensive and cleaner ethanol)



Brian A. J. Salchert    2008-04-19

sw00864sl13-this.lyrics

This Being I Am


Wherever I wander;
wherever I flee /
the Lord is always
after me.

Wherever I wander;
wherever I flee /
the Lord is walking
ahe-ead of me.

    It keeps its mystery
    however I ponder.
    It keeps its mystery
    however I plead.

    It keeps its mystery
    however I wonder.
    It keeps its mystery
    however I weave.



Brian A. J. Salchert    2008-04-19

sw00863d21

d = disposition


Death to any human who does not believe as I believe
is an evil perception fanned by desperation and anger
allowed to heat to the level of hate.  Such, whether
based in a theology, a philosophy, a psychology, or 
a whatever, is self-serving, and cares not about the
common good.

If all you can do is pray, do that.

-

Over at Common Dreams:

"The Unmaking of the Market" by Sally Kohn
Read it and also scroll down to the Galen April 16th, 2008 
12:04 pm comment and read its final paragraph.

"Carter Calls Gaza Blockade a Crime and Atrocity"
This is a Reuters article by Jonathan Wright.




Brian A. J. Salchert    2008-04-18

sw00862v-43.poem41

Venturings



 World Without


What it was and why it was no one knew.
For unknown years it had been there.
Unbothered, it seemed/ it could stay/ centuries more.

Building, mountain, boulevard, trail, the sun rolls round
while over snow south of its range a Snowy Owl
rises/ off a fence post/ and floats beyond.

Neither time, nor reason, nor an empty heart
jostles the neurons of desire in this fantasm.
What lingers, lingers; what departs, departs.  Nod.



-
Brian A. J. Salchert

sw00861d20-campaign

d = decision


 If no changes that matter have occurred, when voting day
for the next president of the these endangered United States
comes, Senator John McCain (a politician I have liked at times
over the years, but for whom I/ will not vote then) will be the
Republican candidate; and either Senator Barrack Obama or
Senator Hillary Clinton (neither of whom is a politician who 
sells what I would prefer to buy then) will be the Democratic
candidate; and there will be outsider candidates.

If someone could prove to me that an outsider candidate I
would be willing to vote for then/ will have at that time a
reasonable chance of winning, I would vote for that person.
Yesterday over at Common Dreams I read 
Obama Is Right by Katrina vanden Heuvel
and many of the comments.  In one of those comments was
the conclusion that a vote for an outsider candidate would in
effect be a vote for McCain, that is if/ that vote/ would have 
been cast for the Democratic candidate otherwise.  I agree.
Therefore, aside from not voting, I will vote for whichever
senator is the Democratic candidate.

The central reason men gathered to form this nation was
the tyranny of King George III.  What besets this nation
now, and indeed the world, is oligarchic tyrrany based on
the so-called free market system.  President Eisenhower,
who had he felt as comfortable in his statesman role as he
felt in his military role (difficult as that was) would likely have
made some significant salutary changes, warned us about
this.  Given how insidiously the ruling powers have trapped
those being ruled, it is hard to know what to do about our
incarceration.  After all, it is not totally odious.  One could
make, little by little, moves toward self-sufficiency, and wait
for the overlord system to collapse; but then what?  One
could hasten its downfall by supporting only the clean and
green, of which ethanol is not a part.  See Care2 but avoid
its petitions area.  One could help promote, organize, and 
then convene a Peoples Congress.  I, for one, would like to
know what those who do not vote and those who've been 
disenfranchised think, even if as a group their opinions mirror
the opinions of those whose votes do count.

Two aspects of collusional oligarchic power which sadden
me most are how easily it can eliminate what threatens it 
and/or how easily it can co-opt an adversarial creation.
Alexander Hamilton was killed by Aaron Burr in a duel, but
Hamilton's spirit (wherever it is) must be so excited it's
about to pop/ out of its hiding place.  At Wikipedia is this
quick biography of Hamilton.  



Brian A. J. Salchert    2008-04-15

sw00860d19

 d = destiny


 Globalization 101

 Global Policy Forum



Brian A. J. Salchert    2008-04-13

sw00859d18-USA

 d = deliberation


 Since I can't do it in person, am thinking about touring online.
Have no plan as yet.  May start with overviews.  Satellite 
images of some U.S. cities.

Thanks to a 4-11-08 link on Linh Dinh's Detainees 
to an article by one Ted Gup, 
I'm changing direction.

This is a timeline history of the U.S. Civil War.
-
current U.S. cabinet
-
U.S. Supreme Court
-
U.S. Senate
-
U.S. House of Representatives
-
1952 U.S. presidential election


With thanks again to Linh Dinh, who placed a link to the following
in a comment to me on his blog.  Read this:  
"The Great American Media Mind Warp" by Joe Bageant.



Brian A. J. Salchert    2008-04-12

sw00858ut-37.poem

The Undulant Trees

   [ Note: One should not laugh at another's misfortune.
      The content below popped into my head several days back,
      and does not relate to any familial event in my life. ]


 Out There


I laughed when my fa-ather
lost his shoe.
I laughed when my fa-ather
lost his shoe.
I laughed,
and laughed,
and laughed,
and laughed.
I laughed when my fa-ather
lost his shoe.

I laughed when my fa-ather
lost his shoe.
I laughed when my fa-ather
lost his shoe.
I laughed,
and laughed,
and laughed,
and laughed.
I laughed when my fa-ather
lost his
shoe.




-
Brian A. J. Salchert

sw00857d17

 "The Ideology of American Empire"


 "737 U.S. Military Bases = Global Empire"


 PBS Frontline: Understanding The Book of Revelation




-
Brian A. J. Salchert    2008-04-08

sw00856d16

 The Death of Due Process



Brian A. J. Salchert    2008-04-07

sw00855d15

 d = diary

 11 steps to a better brain at NewScientist is--
even though from 5-28-05--a worthwhile read.

"Why the demise of civilization may be inevitable" by Deborah MacKenzie 
is also at NewScientist, but you need to subscribe if you
want to read the full article.  Here is one available sentence:
"It appears that once a society develops beyond a certain
level of complexity it becomes increasingly fragile."




Brian A. J. Salchert    2008-04-06

sw00854d14

 Partly because it may not be available much longer,
visit this journal: Isaac Stolzfuts' Journal  Its author
has been missing since about August third of 2007.            
He was 87 at that time.

 Have been involved with a math project based on Pascal's Triangle,
its fourth row to be exact.  It's a different way of looking at the
6n Elimination Table, a table which begins with the 5 7 pair, rising
through all the odd natural numbers which are not divisible by "3".
Thus the next three pairs are: 11 13, 17 19, 23 25.  The second
row of this triangle is comprised of all the natural numbers except
"1".  1 is the number which borders two sides of the triangle, and
"0" is not in the triangle.  The triangle's third row is comprised of
numbers in the natural number summation sequence, beginning
with "3".  I have done what I set out to do with these numbers.
This is all I'm saying about it.



Brian A. J. Salchert    2008-04-05

sw00853d13

 Other than a brief post at Rho-, today has been an online reading day.
Went to Robert Peake's site--though I'd been there late last night--to
read his "Post-Postmodernism And Hope" entry again.  Because his
thoughts speak to me aesthetically and as a human through his words
about Paul Celan and Umberto Saba (a poet new to me but one who
was able to choose life over death against the ravagings of WW2), I
am encouraged by them.

Also revisited the "Performatism, or the End of Postmodernism" essay
by Raoul Eshelman which relates to Robert Peake's entry, but which I 
searched for separately.

At Silliman's Blog for April 04, 2008, is a link to an interview of
Rachel Blau DuPlessis by CA Conrad I had to read in two sittings.
Course work, but of an essential nature.  I then went to Jacket 35
and read her Draft 88 and Draft 89.  Revelatory.

Read a few other poems and parts of poems in that issue, but as
has often happened during the last 12+ months, I was not moved
by them other than toward ennui, a state I suspect reading many 
of my poems would induce: which says less about the poems than
it does about the reader.  Sometimes I wish I lived in Philadelphia
instead of most of the places I have lived in.  But complaining is
such a deadening act.

Was at Latta's Isola too, which today was extra terrestrial.   




Brian A. J. Salchert    2008-04-04

sw00852d12

 Just had enough time this morning to change the dates in 
All About Me and to check the weather map.  It is now
4:30 PM and overcast, but rains seem to be angling in
from Oklahoma City.  Could go mostly south and east
of Springfield.  So far, most of my day was away from
here.  Had to get ready to go shopping, and when that
was done, had to eat while putting the items I bought in
their proper places; and also deal with other needs.  Best
benefit I got was exercise.



Brian A. J. Salchert    2008-04-03

sw00851d11

 Rest of today and all of tomorrow are expected to be stormy.
May not be online much, if at all.  Plan to go grocery shopping
tomorrow.  If that happens, beets and lima beans will be at the
center of my food changes.  Will be pulling away from dairy
products and processed meats.



Brian A. J. Salchert    2008-04-02

sw00850d10

 Partly cloudy with brisk cool winds.  Took two photos of the
blooming sturdy bush.  My sister then took me to where my
general practitioner is so I could have blood drawn for two 
tests.  We also went to the closest library where I requested
two books.  After that we drove around a Wendy's because
I wanted one plain baked potato.  And then, and then, and
then, and then, and then, and then, and then, and this.  Did 
you get all that?

 This is a good site to read whatever of
if you want information about healthy foods
such as lima beans.



Brian A. J. Salchert    2008-04-01

sw00849d9

 From 3:14 PM beyond 5:30 PM/ thunderstorms were coursing
through this city.  For most of that time I had my computer system
unplugged, but I had slowly been constructing a post over at my
Rho- blog, and so I was constantly checking the online weather
map I use; and when it appeared there would not be much more
rain, I went back on and completed my post.  Have been trying
to rid myself of stacks of old mail, and that is the project I was
working on during the storms.  Early on I saw the thickest bolt
of lightning I've ever witnessed zap in the distance, and for a
short while the winds were whipping the rain nearly flat.  Three
tornadoes did some damage in and near small towns.  One farmer 
was blown about forty feet through the air, but dropped into soft
grass.



Brian A. J. Salchert    2008-03-31

sw00848d8

 Good morning.  My being here is a bit of a surprise
since thunderstorms passed through Springfield during
the night and today and tomorrow are forecast to be
rain days.  This is the first Sunday after Easter.  Went
back to reading my Lawrence Grant White translation
of Dante's Comedy.  Read seven sections of the
Paradiso.  Also read some more pages of Art and the
Intellect by Harold Taylor.  Both of these books I have
read before, but years ago.



words from one of my unpublished journals

 Each human is unique.  Each human is a creature who thinks and
a creature who feels.  And some of the deepest human feelings
are fueled by beliefs: beliefs that should not despise uniqueness,
but often do; beliefs that should not cancel thought, but often do.
I know that the ability to feel is just as necessary for our species'
survival as the ability to think.  I know the reptile brain in each of
us is quicker to act than the new brain.   //   But I also know that
howevermuch the flames of feelings, and all too often negative
ones, rise from our moralities, the cores of the great moralities
of this planet favor the flames of positive feelings, feelings possible
only for those who are able and willing to honor thought: Jesus
of Nazareth's, for example, when He urges us to love not only
our neighbors but also our enemies.  Please: whenever you and
I disdain others, we first of all disdain ourselves; whenever you
and I disdain others, we are saying that it is all right for others 
likewise to disdain us; whenever you and I disdain others, we join
those forces that disdain humanity.  The less we are willing to
live with each other, the more we will have to die with each other.

                                                                                    1983




Brian A. J. Salchert    2008-03-30

sw00847d7

 Here's some information about daily water, sodium, and potassium intake
from an August 2004 post at News-Medical.
-
 Here's an alkaline/acidic foods chart
from the Wolfe clinic.



Brian A. J. Salchert    2008-03-29

sw00846d6

 Last night late while winds whoed into & under my bedroom window/
I read 12 and 13 of Dante's Paradiso.

 As usual, I spent much of the day bouncing from blog to blog,
leaving a comment at one of them.  Also did some research on
the "intentional fallacy' and the "affective fallacy" as I needed to
refresh my memory.  Slowly I am getting recharged regarding
poetics.


Nada Gordon interviews Benjamin Friedlander



Brian A. J. Salchert    2008-03-28

sw00845d5

 Matthew Barney is a sculptor who has had what I class as a
charmed life.  See Wikipedia article.
 From www.sfmoma.org
this about him:
". . . exploring the notion that form emerges
through struggle against resistance."


* thank you, l. q.



Brian A. J. Salchert    2008-03-27

sw00844d4

 The last two days a post at a blog I visit has moved me to comment twice
beneath that post/ and to spend several hours last night researching via G-
the topic "immanent critique"/ and also to add links in my Rho- list to two
.com sites.  Since around WW1 this planet has slithered into a cavern of
contradictions of such force that the gyroscopes of the teeming humans
upon it are consistently askew.



Brian A. J. Salchert    2008-03-26

sw00843d3

 Have been busy with other projects the last several days.

 This morning at money.aol.com/ this:
Most Common Tax Scams

 Placed the final page of brians brain 2000 up yesterday 
on my bajsalchert blogspot blog.

 Have been reading many things online, and posting comments.
Most of that has been done at poetry blogs, particularly the
Poetry Foundation Harriet blogs.

 If you would like to read and vote on poems, Andrew Shields has an
ongoing project for doing so.



Brian A. J. Salchert    2008-03-25

sw00842v-42.poem40

Venturings



 The Guardian


How shall he sing with dangled tongue
Our vibrant warrior roundelay;
War in rags and sleep in dung;
Scurry as though the bees had stung,
When we are other cares away?
"How can his back be glad, though wrung,"
Where he must sing with dangled tongue
Our vibrant warrior roundelay
And pommel jungles in dismay
Or cough up sand from stifled lung
Or butted, fall to naked clay?
Oh how in that foul disarray,
How shall he sing with dangled tongue
Our vibrant warrior roundelay?


                                        (????)



-
Brian A. J. Salchert

sw00841v-41.poem39

Venturings



Holy Saturday 2008-03-22


And though He had
not yet risen,
the Lord Jesus
went to that place
wherein He would
interact with
certain waiting
human spirits,
telling them that
the time was near
for them to be
taken from there
into that realm
beyond the need
for patient hope
and ardent faith

And I am not
and I am not
and I am not
and I am not
and I am not
and I am not
and I am not
and I am not
and I am not
and I am not
and I am not 
and I am not
and I am not
and I am not
until I am
alive in Love



!
Brian A. J. Salchert

sw00840d2

 Not all blog previews are trustworthy.
The preview where my other blog is does not tell the truth.
The preview where I regularly comment does not tell the truth.
Why?  Those who programmed those previews ought to know,
and they ought to know how to program them so they tell the truth.
Although I can learn how to work around such faulty previews,
previews which do not tell the truth irk me.
Given these facts, it is just as well AOL Journals
does not provide previews.



Brian A. J. Salchert    2008-03-21

sw00839d1

 Sprintedon Tracker has been discontinued.

 Diary, though it may not be daily, is replacing it.       d = diary

 In mulling over projects, there's a chance I may stop posting 
poems of mine after I sense Seminary, The Undulant Trees,
and Venturings have ended.  Have begun a new project, but
it will remain a penned poem.  Am not even sure I will be able
to complete it.

All day Tuesday it was windy and rainy with scattered storms.



Brian A. J. Salchert    2008-03-20

sw00838st100-Palm.Sunday

Read the Gospel of Matthew   26.36 - 27.60



__|__
   |
   |



                                                                        Entry2649

                     [ Note: 26 + 36 + 27 + 60 = 149 = 100 + 49 ]

                    [ Note: This weekend I remained in my apartment,
                               but I brought the missal I had been given
                               when I was in a Jesuit Noviate 46+ years
                               ago/ into my den/bedroom, and placed it
                               at the foot of the bed.  At that point in the
                               reading where Jesus expires/ an instruction
                               tells one to kneel and pause.  I, carefully,
                               knelt, and then looked up.  The time on/
                               the clock I've placed on the bedboard's
                               top shelf/ was 1:10 PM.  At 1:11 PM I
                               carefully rose.  For those of you who do
                               not know this about me: some years back
                               1:11 (both AM and PM) became for me
                               God times. ]  

sw00837ut-36.poem

The Undulant Trees




 5 AM



In the distance
herorrrrrm     herorrrrrm

a coal train passing
through Springfield MO


and then nearby
cheep     cheep     cheep

a robin
wakes the night


& I
I keep
my self in bed

white
low
brown eyes hid




-
Brian A. J. Salchert

sw00836sl12-dark.lyrics

 Dark
    (The End of a Culture)


Rats' tails
rats' tails
they're comin'
they're comin'
e-e-e-e-e
NO!
they're comin'
dark

I saw 
a bloodied baby,
his left ear
almost gone;
his throat
a punctured song.

   And whistles
   fly
   from the corner bricks,
   and dead leaves
   freak
   in the wind.

A man
in white and crimson
has turned down
7th Ave.;
he knows
just what I have.

It won't
buy me a ticket
to God or
get me home;
its clouds
blot out the sun.

   And whistles 
   fly
   from the corner bricks,
   and dead leaves
   freak
   in the wind.

Some say
the Beauty's coming,
some say the
Devil's Beast;
some fast,
some splurge and feast.

Some think
a dude like me should
be pummelled
dead as dust;
some think
that I should run.

   And whistles
   fly
   from the corner bricks,
   and dead leaves
   freak
   in the wind.

The news
is spread for garbage
and stuffed in
drafty holes;
our heads
have lost their souls.

The church
that makes the money
is still thought
number one;
but this MAN
tradition's done.

   And whistles 
   fly
   from the corner bricks,
   and dead leaves
   freak
   in the wind.

I saw
a bloodied baby,
her right ear
almost gone;
her throat 
a punctured song.

Rats' tails
rats' tails
they're comin'
they're comin'
e-e-e-e-e
NO!
they're comin'
dark



                    1974-11-30     Brian Salchert


2008-03-11

sw00835sl11-friends.lyrics

 Friends


   Morning glories
   climbing high,
   patterned pieces
   of the sky:

   oh
   why
   do I,
   dear, find
   them so
   entrancing
   when
   ev'-
   ry day
   I see
   them soft-
   ly dancing?


When we were both
in seventh grade
I barely knew
my body's ways,
so made it seem
I wanted you
and no one else.


   (Chorus)


When we were both
in junior high
my body knew
it wanted guys,
but couldn't make
my heart believe
that wasn't hell.


   (Chorus)


Now we have both
to each to each
been married for
ten altered years,
and I am out
but still with you
for we are friends.


   Morning glories
   climbing high,
   patterned pieces
   of the sky:

   I
   know
   why I,
   dear, find
   them so
   entrancing
   though
   ev'-
   ry day
   I see
   them soft-
   ly dancing.


                             1975     Brian Salchert


2008-03-11

sw00834sl10-lucy.lyrics

 Lucy


Well
he found her in the back
where the railroad track
took a little turn
and the switch engine came
and the switch engine went
at a slow burn
and you could
hear its whistle
every time
for the road ahead
and the road behind
but you'd never know
when he would be seen
with his Lucy again

   Oh oh oh
   bubbles in the water
   bubbles in the air
   I had some dreams once
   I wanted to share
   but just as I woke up
   bang bang bang
   they popped

Now
he thought that was her horse
that had eased off course
chewing flowers down
where the Sims' gulley fell
near his dad's town
and you could
hear it whistle
every while
like a fear that stares
or a fear that smiles
but you'd never know
when he would be seen
with his Lucy again

   (Chorus)

Yes
he kissed her in the field
while the tractor's wheels
toasted in the sun
and the boys happened in
and the boys happened out
with their toy guns
and you could
hear them whistle
every night
for the dream begun
for the dreaming done
but you'd never know
when he would be seen
with his Lucy again

   (Chorus)


                        1975     Brian Salchert


2008-03-11

sw00833sl9-say.hi.lyrics

 Say Hi to the World



      (Chorus)

         Say
           hi
      to the world
         Say-ay
           hi
            hi hi hi-i

         Say
           hi
      to the world
         Say-ay
           hi
            hi hi hi-i


There's a blue sky rising
there's a warm breeze playing
there's a good day rolling
there a new bird preening


      (Chorus)


There are bright eyes talking
there are sweet tongues kissing
there are wise hearts telling
what is worth our keeping


      (Chorus)


There are people moving
there are people standing
there are people marching
there are people spending


      (Chorus)


There are times to fathom
there are thoughts to open
there are dreams to father
there are wills to ocean


      (Chorus)


I will spring my being
and become full summer
then in fall walk blazing
to my mystic winter


      (Chorus)

      (Chorus)



                              1975     Brian Salchert


2008-03-11

sw00832sl8-young.ones.lyrics

Young Ones I Knew Who Died



My father
asked me
who had chopped
on the maple
I looked
at him
in surprise
We found out
& I told him
I would tell them
we were angry
& that they'd have to
chop it all down
if it died

But I only
told Bob
not Jerry
and later
that summer
he was gone
He had fallen
to leukemia
in the bed house
a baseball
trophy
by his side

  A young one 
  I knew
  who died


Some summers
later
another Jerry
out in left
The last time
I saw him
in the sky
He had jumped up
to snag
a zinging baseball
What a wonder
His catch
sparkled
in the eye

But a few
days after
he was hunting
when suddenly
he stood
in the boat
and his uncle
accidentally
let his gun fire
a bullet
in the back
of Jerry's coat

  A young one
  I knew
  who died


Now last night
my Janice
reading somewhere
in the paper
found a Dale
who had worked
at the inn
A skier
I remember
as she told me
where he'd gone to:
near Slinger
at Little
Switzerland

And I wonder
what went
through his head
as the truck
rumbled closer
to their car
though I know
what he wished
may not matter
and the living
need to live
with their scars

  A young one
  I knew
  who died

  Young ones
  I knew
  who died


          1975     Brian Salchert


2008-03-10

sw00831v-40.poem38

Venturings



 Commencement


Still must I contend with vanity, and lose.
For certain matters matter past all will,
And though a poet would desire to die
In purer worlds and there renew his life,
The paradox reverses in its time.
So days like this bring scratchings on a page
With more important scribblings of mistakes,
What then?  But questions are irrelevant,
The patron says.  And so this little frame
Sweats out its dusty task and cultivates
A desert for his race, and so this youth
Expends some thousand minutes swinging blanks
Against a vaporous crowd; and so, at last, 
He really dies (his brothers will not miss
Him though a few may hang his picture on
Their inner walls); yet there's the patron, friend,
And even if I were an angel low
There'd be a ceiling to repair, a cell
Which I could not escape but by a hard
And satisfactory epic sky and cramps
An old marine would rather not recall.
But I procrastinate, as all our pseud-
O intellectuals say.  I must begin.

Four years for most; still, nothing has an end,
And we are what we make and what makes us;
And if our senses slice through every realm
Or every realm attacks and slashes them,
Those days that rolled the snow across our eyes
Or dropped the sun a certain million miles
Are both our gain and never once our loss.
How I despise these platitudes I raise
Though they may well be truer than we feel
(A spider's web could say as much; perhaps
Much more); but there's the patron, sir, and though
A mallow or a friendly wink would soothe
In better ways anachronistic bones
As these of mine, the world must check and mate
Me if I ever hint at such a move.
A grave iconoclasm now prevails
Which, somehow, each of us must shatter out:
But there are years and trees and many births--
Yet not a billionth of a spark of time--
For us.  So where is our commencement won
If not beyond these wrinkled vines, if not
Beyond these growing stones, if not beyond?
Someone will speak of orbs to us, but we
Do not want orbs but herbs; but we do not
Want herbs but love: learning all our lives.


                                                (1965-1982)



-
Brian A. J. Salchert

sw00830v-39.poem37

Venturings



 Stages


One day when I was tricycling free through air
And summer came the "whom" of drums, the "where"
Of brass.  Wonder wheeling response to both,
I prayed they would march till distance was bare;
Prayed they would march till melodious growth--
Mysterious as the varying shade
I peddled through--could no longer be loath
To share its faraway goads, goads who played
Near railroad yards in suits of blood and blade.

And again today I remember fields
Whose star-white blooms brought o strawberry yields
We sunk ourselves into with laughing joy;
We plucked, we pressed, we smeared.  How wild the wields
Of berries crushed!  How cool and pink each boy!
Neat screams: chaste girls who ran through weeds; who fell
On clumps of razor grass: new queens of Troy
For us to save, new tears to wipe on hell.
How soon we lost our hearts beneath that spell!

So, as eleven solar orbits turned
Me toward a special pine, those hopes I spurned
On music's board began, somehow, on art's 
To climb; and I, rejoicing, deeply yearned
The miracle of canvas life.  My heart's
Impatience gathered oils.  My fingers strained
For the mixing knife; grasped released the darts
That tell. . . .  And so I brushed and stained
My tree: all that was lost; all that was gained.

But time allowed another turn, and I
Allowed my paints to crack till knowing why
The notes would not; nor would the brushes' strokes,
Long last.  For days this self, a foreign sigh,
Appeared to be, as if a webbing's spokes
Destroyed by some invader hard about
And the webber forced to hide, spinning jokes
For its survival, jokes which could not shout:
Each word must be a pebble ringing out.


                                                         (1964-197?)



-
Brian A. J. Salchert

sw00829ekua-page15

Edges of Knowledge


Thursday 2003-08-28
-
Passing through difficult hours (days).

After eating my "Meals on Wheels" gift this noon, I
made a second call to J. L. at E. S., telling him I was
about to take a rest because I was still tired from the
9:15pm Tuesday and the 9:15pm Wednesday difficulties--
all of which may be true but now seems to me not
accurate in the details/ as I "think" I am getting my days
mixed up.
  At 3:11pm I was awakened by tromping winds.  I noted
the A/C was on and a small branch with new leaves from
my "drop-drop" tree was in the lot next to the back steps.
That the thermostat temp read above 80 surprised me
some since I felt cold, but I let it be.  I went to the den,
then into the restroom; then unplugged the three lines I
routinely unplug when a heavy storm is about.  I then
got into my jacket and returned to the kitchen/ where I
opened a tube of Ritz crackers, removing eight to a bowl.
Back in the den/ I took my multivitamin with water and
those crackers.  The storm tromped on and no new one
seemed likely to take its place; so at 4:11pm I plugged/
up again.

Saturday 2003-08-30
-
Janice--several years ago--told me to throw away the 2
heart-shaped Valentine balloons on sticks/ I had stationed
at the top corners of the metal shelving here in the den
nearest the doorway to the living area/ no matter they had
not in the least deflated.  (The Sam-set for 4:14pm Topamax
watch is waking the creatures asleep on the sofa-bed.)  At
last I did: first to a waste basket near the TV, and today to 
the large kitchen basket, where--after a time--I removed
their sticks, lightly knifed their internal inflations, and
quartered their poles.

  Pride, Jesus, You know how I am beset with/ a dikydak
pride.

Monday 2003-09-01
-
Admittedly, I had been considering doing so for some
time, but yesterday--by a curious yet binding turn of
activities, I took my spirit to St. Augustine and his
Confessions.
  The web-site I decided to enter--.  If it happens you
are not aware 32 is a central number in my life, and, 16,
collaterally is--.  According to the information given
there, Augustine of Hippo was 32 when he became a true
Christ-follower--a conversion his mother St. Monica had
been praying for for many years--and also that one of the
chapters in his autobiofraphy centers on his 16th year.

Sunday 2003-09-14
-
[ Note: this entry consists of two poems, both of which
          are now in my in-progress Venturings book of
          mostly poems.  Therefore, I'm going to place links to
          each of them here instead of placing each poem here. ]

A Cardinal of Consciousness

***** *** *** *****

Sunday 2003-09-21
-
Yesterday, after not having done so in a long while,
I washed my hair; and J. C., with the aid of another,
started building a shed.  I'd planned to go out, but I
was so tired.  I fell asleep several times during lunch.
One time/ I tried to highlight/ a few front hairs with
sardine oil.
  It didn't occur to me until today that 9, 20, & 3
add to 32, and 32 adds to 5.
  I have a semi-habit of checking the heat pump
thermostat before going to bed.  Sometimes I
turn it off.  I don't have it set to blow warm.
Normally it will start between 10am and 1pm.  I
knew it was going to much sooner this morning
because the temp stayed high last night.  At 7:11
(by this den's clock) it came on.
  Sprinkles!: 10:39am.
  Three scoops of yogurt and a slice of blue pie
replaced my usual breakfast this morning.
  Another strange day: as most are.  I might
be back.

Friday 2003-09-26
-
                                 Nothing 


-
Brian A. J. Salchert

sw00828sl7-a.snow.song.lyrics

 A Snow Song


The snow is falling,
     The snow is falling,
Like white fluffy quarters
     All over the ground.

The snow is falling,
     The snow is falling,
Like white fluffy quarters
     All over the ground.

The snow is falling,
     The snow is falling,
Like white fluffy quarters
     All over the ground.

          I want to go out,
               And I want to play.
          I want to dance in
               The sno-ow today.
          Yes, I want to go out,
               And I want to play-ay-ay,
          And I want to dance in
               The sno-ow today.
                    I want to prance in
                         The sno-ow today.
                              I want to angel
                                   The sno-ow today. 



[ The above could all be repeated three times, but not necessarily 
    the same way musically.  There's a melody in my head for this
    which--as it usually does--came before the words did; however,
    that melody (even with its last line changes) may be the melody
    for a song whose words I don't remember.  I at first thought 
    it might be a song whose words were in German.  This song's
    words (lyrics) began arriving shortly after 7:30 AM, and its
    title came later.  While I was looking out my bed den window
    after 7 AM/ fluffy flakes did fall. ]

                                                          Brian A. J. Salchert
2008-03-04
 

sw00827ekua-page14

Edges of Knowledge


Sunday 2003-06-29
-
For the last several years now, I have been trying especially hard
to identify the Lord's passing (i.e., of-the-moment) signals to me,
particularly when a harmless error is involved.  Sometimes, I feel
in my heart, I do identify His signals.  Last Thursday, however, on
the van ride home from Epilepsy Services, I--as I see it now--    
failed to.  It happened there was another passenger.  Usually I am
the only one.  It also happened the driver had never taken me
home before, and so was in need of a few directions.  Then the
passenger called out/ she was bleeding and wanted to be taken
back, but the driver told me the place she had come from was
now closed.  Then the driver missed a turn, and I told her she
did/ immediately; so she zipped into a parking lot to turn around.
There: we were being shaded by some/ rather large trees, and 
there is the place where I/ missed my Lord's signal.  I should have
had the driver stop for a few seconds/ if I could not get right away
what my Lord was telepathing.  Even though the drive from there
to where I live is short, I feel I ought to have talked the van driver
into checking the woman passenger's bleeding/ at that place.

Friday 2003-07-11
-
6pm is nigh, and I am feeling hungry again.  Do not know what it is,
but every Friday lately I find myself thinking it is Saturday, or even
Sunday.  This Friday I actually did get to Publix.  After I finish eating
I will need to return to my letter to jls.  I realize God may take one
of us from this plane before any new connection between us occurs.
One paragraph in that letter may soon no longer be there, but it will
be here.  Yes, it is a paragraph about me.  
   *     *     *
   Planets, words, numerals: I was still so held
   by the urge to be a philanthropist, I flatly 
   ignored my lack of all the character traits
   required.  Then my health declined.  Thus,
   instead of being of service to other, as I
   would have preferred, others have been (and
   continue to be) of service to me.  I feel sure
   it didn't need to be this way, but it is; and
   God is, as enigmatically as always, unimaginably
   good to me.  Certainly I/ am not right, if I 
   ever was.  (Sister knows.)  Nonetheless, with
   my Early Retriement Social Security and the
   local services I am allowed to use, I am getting
   on reasonably well.
   *     *     *

Saturday 2003-07-12
-
Just as the final revision of my letter to jls finished printing/
several gusts of warm humid wind reverberated against 
this place and into & through the nearby trees.  A space
in me wanted it to mean something, but I could not tell if
it did; and if it did, if it meant good or meant ill.

Sunday  2003-07-13     4:59pm
-
All day grey upon grey with only a speck of blue now and
again given the chance to show through; and a smidgen of
rain, and later another dildy-dash; but now the threats and
the foolery are gone; a real wash takes the air, enters the
ground.  Less than 15 minutes.  Still, it was and did, and
my half-thought of a weed eater venture has shrunk dead.

Thursday  2003-07-17
-
  Several nights ago I washed dishes out of need.
I had used all 16 pieces of regular silverware; but,
having used my original washing routine, those 16
pieces were all I had left to wash.  At that moment
I decided to take a break.
  Recently I had gotten into the habit of washing the
4 tablespoons, which are made differently, last.  Also,
I usually washed 3 together.  Since they are under
soapy water, I never know which 3 will come up 
together.  Knife, fork, spoon.  Knife, fork, spoon.
Knife, fork, spoon.  And: necessarily: knife, fork,
spoon.  Finally, with the last 2 tablespoons up and
dried, I raised my head, and caught 9:11.  The next
digital was 9:12.  Too strange.

Saturday 2003-08-16 (moving past 4pm)
-
The entry below was originally--but differently presented--
in The Blue Ledger.

If I am
allowed in,
I might become
Heaven's Dunce,
or one of them.
-------------------- Today is Saturday:
--------------------    but at 2:34am.




-
Brian A. J. Salchert