entry 17tpo = termposition [ note: in this sequence, the subtrahend square root = the tpo ] [ note: minuend square root + subtrahend square root = remainder ] [ note: each term in this sequence is a positive odd whole number (pown) ] [ note: had this sequence begun with 1² - 0² = 1, the minuend square root would have equalled the tpo ] 2² - 1² = 3 3² - 2² = 5 4² - 3² = 7 5² - 4² = 9 = 3² 6² - 5² = 11 7² - 6² = 13 8² - 7² = 15 = 3 x 5 9² - 8² = 17 10² - 9² = 19 11² - 10² = 21 = 3 x 7 12² - 11² = 23 13² - 12² = 25 = 5² 14² - 13² = 27 = 3 x 9 = 3 x 3² 15² - 14² = 29 16² - 15² = 31 17² - 16² = 33 = 3 x 11 18² - 17² = 35 = 5 x 7 19² - 18² = 37 20² - 19² = 39 = 3 x 13 21² - 20² = 41 22² - 21² = 43 23² - 22² = 45 = 5 x 9 = 3 x 15 24² - 23² = 47 25² - 24² = 49 = 7² 26² - 25² = 51 = 3 x 17 # re: 3² tpo 2 and tpo 4 1 x 4 = 4 also: 2 + 4 = 6 re: 5² tpo 4 and tpo 12 3 x 4 = 12 also; 4 + 12 = 16 re: 7² tpo 6 and tpo 24 6 x 4 = 24 also: 6 + 24 = 30lunch break[ note: (2 x 4) + 1 = 9 (4 x 6) + 1 = 25 (6 x 8) + 1 = 49 ] # 27² - 26² = 53 28² - 27² = 55 = 5 x 11 29² - 28² = 57 = 3 x 19 30² - 29² = 59 31² - 30² = 61 32² - 31² = 63 = 7 x 9 = 3 x 21 33² - 32² = 65 = 5 x 13 34² - 33² = 67 35² - 34² = 69 = 3 x 23 36² - 35² = 71 37² - 36² = 73 38² - 37² = 75 = 5 x 15 = 3 x 25 39² - 38² = 77 = 7 x 11 40² - 39² = 79 41² - 40² = 81 = 9 x 9 = 3 x 27 42² - 41² = 83 43² - 42² = 85 = 5 x 17 44² - 43² = 87 = 3 x 29 45² - 44² = 89 46² - 45² = 91 = 7 x 13 47² - 46² = 93 = 3 x 31 48² - 47² = 95 = 5 x 19 49² - 48² = 97 50² - 49² = 99 = 9 x 11 = 3 x 33 51² - 50² = 101 52² - 51² = 103 53² - 52² = 105 = 7 x 15 = 5 x 21 = 3 x 35 54² - 53² = 107 55² - 54² = 109 56² - 55² = 111 = 3 x 37 57² - 56² = 113 58² - 57² = 115 = 5 x 23 59² - 58² = 117 = 3 x 39 60² - 59² = 119 = 7 x 17 61² - 60² = 121 = 11 x 11 # [ note: if zero is included in the natural number summation sequence, any pown square minus 1 will equal a pewn which (when divided by 8) equals a term in the nnss -- example: 81 - 1 = 80; 80/8 = 10 as in: 0 + 1 = 1; 1 + 2 = 3; 3 + 3 = 6; 6 + 4 = 10 ] # 4 or (9 - 1)/2 or (3 x 1) + 1 = tpo for 3 x 3 8 4 12 or (25 - 1)/2 or (5 x 2) + 2 = tpo for 5 x 5 12 4 24 or (49 - 1)/2 or (7 x 3) + 3 = tpo for 7 x 7 16 4 40 or (81 - 1)/2 or (9 x 4) + 4 = tpo for 9 x 9 20 4 60 or (121 - 1)/2 or (11 x 5) + 5 = tpo for 11 x 11 24 4 84 or (169 - 1)/2 or (13 x 6) + 6 = tpo for 13 x 13 28 4 112 or (225 - 1)/2 or (15 x 7) + 7 = tpo for 15 x 15 [ note: 4/1 = 4 12/2 = 6 24/3 = 8 40/4 = 10 60/5 = 12 84/6 = 14 112/7 = 16 and (1 x 2) + 2 = 4 (2 x 2) + 2 = 6 (2 x 3) + 2 = 8 and so on and (3 - 1)/2 = 1 (5 - 1)/2 = 2 (7 - 1)/2 = 3 (9 - 1)/2 = 4 and so on and 9 - 1 = 1 x 8 25 - 1 = 3 x 8 49 - 1 = 6 x 8 81 - 1 = 10 x 8 121 - 1 = 15 x 8 169 - 1 = 21 x 8 225 - 1 = 28 x 8 and so on ] # And where am I going with this? Wherever it takes me. - As you can see, 105 is an important number. It is what I call a node number. Its being divisible by 3, and by 5, and by 7, is what allows 101 and 103 and 107 and 109 to each be a number divisible only by itself and 1. 15 is a node number. The next such number is 945, if one goes by a calculator; but it comes after 29's power has kicked in. At 105, 11's power has not yet kicked in. If 5 and 9 are ignored, 231 becomes a node number in a different family of node numbers; but any number whose final digit is not "5" is of less interest because 3 divides into an odd number every six numbers, and so would divide into 237; and 5, of course, divides into 235. Actually, what I am trying to do is uncover patterns I had missed on earlier searches. - 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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## Blog Archive

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## Tuesday, February 19, 2008

### sw00816math-about.subtracting.squares

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