entry 18tpo = termposition pown = positive odd whole number pewn = positive even whole number Today am beginning subtraction sequence with 1² - 0² = 1. Am interested in how it is not like the sequence presented in entry 17. 1² - 0² = 1 2² - 1² = 3 3² - 2² = 5 4² - 3² = 7 5² - 4² = 9 = 3² [ note: this puts 9 at tpo 3 and tpo 5 instead of at tpo 2 and tpo 4 -- is this better, worse, or just different? ] [ note: a pown whose only multiples are itself and 1/ never appears above level one in a descension-by-squares sequence/ because it is not a square of any whole number square root ] [ note: the "itself" must be a pown greater than "1" ] 6² - 5² = 11 7² - 6² = 13 [ note: 25 (5²) first appears in a d-b-s sequence as the minuend in the squares' subtraction whose remainder is 9 ] [ note: my personal view is that today's sequence is easier to work with ] [ note: if you are wondering why I am talking about levels greater than level one but am not showing any such, it is because for clarity I have chosen a collapsed form -- explanation: ordinarily a d-b-s declines oppositionally from its major minuend/ so that at its highest level 5² would show 2² as its subtrahend/ and then 4² and so reveal the remainders "21" and "9" and a d-b-s (DF10) consisting of two levels -- not so bad, but at higher levels can quickly get unwieldy ] (revised 02/21/08) [ note: DF = descension family and the 10 = sum of factors in DF for 5 x 5: 5 + 5 or 3 + 7 or 1 + 9 ] (added 02/21/08) Okay/// so inthissequence the tpo will always equal (the remainder plus 1) divided by 2. Therefore, if the minuend square root is 128, the remainder will be (128 times 2) minus 1. I prefer letting the minuend square root be the tpo. Still, there seems to be no easy way to know if a given pown is only divisible by itself and 1. Mathematicians, using a specialized formula, have found such numbers that are figuratively beyond our solar system; but I am interested in something more basic. 8² - 7² = 15 = 3 x 5 9² - 8² = 17 10² - 9² = 19 11² - 10² = 21 = 3 x 7 12² - 11² = 23 13² - 12² = 25 = 5² [ note: each pown tpo (square root) equals the square root of the remainder of that term in this sequence which relates to it, thus 5² finds its equal at tpo 13 or (5 x 3) - 2 ] Here are some examples: - (3 x 2) - 1 tpo 3 and tpo 5 (5 x 3) - 2 tpo 5 and tpo 13 (7 x 4) - 3 tpo 7 and tpo 25 (9 x 5) - 4 tpo 9 and tpo 41 (11 x 6) - 5 tpo 11 and tpo 61 (13 x 7) - 6 tpo 13 and tpo 85 [ note: the matching tpo locations are separated from each other in just the same manner as they are in the sequence shown on entry 17, but are one tpo higher here -- what is 2 and 4 there is 3 and 5 here ] Though I wanted to avoid mentioning facts I have long known, the usefulness of them suggests otherwise. Only odd numbers matter, and among those only those numbers with final digits that are not "5". Any pown whose digits add to 3 or 6 or 9 is divisible by "3". "861" is such a number in that 8 + 6 = 14 and 14 + 1 = 15 and 1 + 5 = 6. Now, there is what I have come to call an Elimination Table (E T) which effectively bypasses all numbers divisible by "3". Am not going to explain that here. However--to continue with more of the obvious, a greater-than-1 pown does not acquire its power to invalidate the primality of other powns until it is squared. "2" is the first prime number, and it is the reason 3, 5, and 7 are prime numbers. "3" is the reason 9, 15, and 21 are not prime #s, but 11, 13, 17, 19, and 23 are. Another way to ferret out the truth about a given pown is by adding squares to it, beginning with 1². This works with "143" since 144 is 12 x 12. Here observation tells one "143" in not divisible by 3, or by 5, or by 7; but must be divisible by two prime numbers. Which two? 1² indicates that whichever two they are they must be 2 apart from each other. So, (12 - 1) = 11 and (12 + 1) = 13. Let's see. Yes.So where are the squares?The squares run along a line separated by the powns in ascending order. From 0 to 1 is 1; from 1 to 4 is 3; from 4 to 9 is 5; from 9 to 16 is 7; but is there a trick of sorts one can use? Am not sure; but do know every pown square is 1 greater than a number divisible by 8, and that every pewn square is divisible by 4. However, something different is teasing my brain. 1/2 = .5; 4/2 = 2; 9/2 = 4.5; 16/2 = 8; 25/2 = 12.5; 36/2 = 18; 49/2 = 24.5 | 2 - .5 = 1.5; 4.5 - 2 = 2.5; 8 - 4.5 = 3.5; 12.5 - 8 = 4.5; 18 - 12.5 = 5.5; 24.5 - 18 = 6.5 | I know: I left my flyswatter on the moon. .5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5 is a run of numbers wherein each greater number is 1greater than the one before it. Have also noted another fact about these numbers, but am not sure about its value. If .5 is allowed to represent 1, 1.5 to represent 4, 2.5 to represent 9, 3.5 to represent 16, 4.5 to represent 25, 5.5 to represent 36, and 6.5 to represent 49, how does one use them? The other fact I noted is that if .5 is added to one of these numbers, the resulting number is the square root of the number represented. That's fine, but is not what I was hoping for. Similarly, 2 times one of these .5 numbers gives us the difference between that number it represents and next lesser represented number; but that too is not what I was hoping for. Hmm: 1 to 5 = 4; 5 to 9 = 4; 9 to 13 = 4 -- this is for 1, 9, 25, and 49. Likewise: 3 to 7 = 4, and 7 to 11 = 4 -- this is for 4, 16, and 36. On the moon? How about on an asteroid. For what it's worth: If the result of dividing 4 into a pewn is a square, then that pewn is a square. - Brian A. J. Salchert

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

## About Me

- brian (baj) salchert
- Rhodingeedaddee is my node blog. See
*my other blogs*and*recent posts*.

## Guide

[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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## Wednesday, February 20, 2008

### sw00817math-page2.subtracting.squares

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