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

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, May 7, 2008

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

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