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 isn- 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

is a tiny wandering imaginary dinosaur which migrated from AOL in October of 2008.

## About Me

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- Rhodingeedaddee is my node blog. See
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[6-16-2009 Update Insert: Most of what is in this space is now moot. I found out what I was doing wrong and have reinstated Archives and Labels searches. They do work. However, in certain cases you may prefer Labels to Archives. Example: 1976 Today begins in November of 2006 and concludes in December of 2006, but there are other related posts in other months. Note: Labels only shows 20 posts at a time. There are 21 hubs, making 21 (which is for 1976 Today) an older hub.] ********************************* to my online poems and song lyrics using Archives. Use hubs for finding archival locations but do not link through them. Originally an AOL Journal, where the archive system was nothing like the system here, this blog was migrated from there to here in October of 2008. Today (Memorial/Veteran's Day, May 25, 2009) I discovered a glitch when trying to use a Blogger archive. Now, it may be template-related, but I am unable to return to S M or to the dashboard once I am in the Archives. Therefore, I've decided on this approach: a month-by-month post guide. The sw you see in the codes here stood for Salchert's Weblog when I began it in November of 2006. It later became Sprintedon Hollow. AOL provided what were called entry numbers, but they weren't consistent, and they didn't begin at the first cardinal number. That is why the numbers after "sw" came to be part of a post's code. ************** Here then is the month-by-month post guide: *2006* November: 00001 through 00046 - December: 00047 through 00056 -- *2007* January: 00057 through 00137 - February: 00138 through 00241 - March: 00242 through 00295 - April: 00296 through 00356 - May: 00357 through 00437 - June: 00438 through 00527 - July: 00528 though 00550 - August: 00551 through 00610 - September: 00611 through 00625 - October: 00626 through 00657 - November: 00658 through 00729 - December: 00730 through 00762 -- *2008* January: 00763 through 00791 - February: 00792 through 00826 - March: 00827 through 00849 - April: 00850 through 00872 - May: 00873 through 00907 - June: 00908 through 00931 - July: 00932 through 00955 - August: 00956 through 00993 - September 00994 through 01005 - October: 01006 through 01007 - November: 01008 through 01011 - December: 01012 through 01014 -- *2009* January: 01015 through 01021 - February: 01022 through 01028 - March: 01029 through 01033 - April: 01034 through 01036 - May: 01037 through 01044 - ******************************************************* 1976 Today: 2006/11 and 2006/12 -- Rooted Sky 2007: 2007/01/00063rsc -- Postures 2007: 2007/01/sw00137pc -- Sets: 2007/02/sw00215sgc -- Venturings: 2007/03/00216vc -- The Undulant Trees: 2007/03/00266utc -- This Day's Poem: 2007/03/00267tdpc -- Autobio: 2007/04/sw00316ac -- Fond du Lac: 2007/04/00339fdl -- Justan Tamarind: 2007/05/sw00366jtc -- Prayers in December: 2007/05/sw00393pindc -- June 2007: 2007/06/sw00440junec -- Seminary: 2007/07/sw00533semc -- Scatterings: 2008/08/00958sc ** Song Lyrics: 2008/02/sw00797slc ********** 2009-06-02: Have set S M to show 200 posts per page. Unfortunately, you will need to scroll to nearly the bottom of a page to get to the next older/newer page.

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## Thursday, May 15, 2008

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

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