entry 19This entry follows from entries 17 and 18. Four squares sequences involving the number "4": 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, n 9, 36, 144, 576, 2304, 9216, 36864, 147456, n 25, 100, 400, 1600, 6400, 25600, 102400, 409600, n 49, 196, 784, 3136, 12544, 50176, 200704, 802816, n Each of these is a pown-square-base sequence. Pewn square roots are found by multiplying by 2 once the initial pewn square root is known. The initial pewn square root in each of these is: 2, 6, 10, and 14. Questions derived from this are: How does such awareness aid in finding squares? Is this awareness worth having? What about the pown square roots? Would square roots / squares tables be all that is needed? Of what importance is all this anyway? What first impressed me was the discovery that each of the odd squares could serve as a base for a sequence of even squares. Next was knowing it is possible to extract a particular odd square from a particular even square. For me all this is an infinite game of a different order. A table of initial odd squares and initial multilplied-by-4 even squares might be useful even if not used beyond those two female/male entries. Just spent some moments seeking a gap, and I found it at 18 x 18, which is not in any of the four sequences shown above. So where is it? I asked myself. Well, 18 x 18 = 324, and 324/4 = 81. So: 81, 324, 1296, 5184, 20736, 82944, 331776, 1327104, n Though I've already stated this in another way, here is what is coming to light: If the square root of the initial pown square is, say, "11", then the square root of the initial pewn square in that sequence which begins with "121" will be "22". 22 x 22 = 484. So: 121, 484, 1936, 7744, 30976, 123904, 495616, 1982464, n Really am wondering now if this is indeed an infinite game, or if there is a repetition point. Haven't passed through 10 cycles yet. The eleventh cycle begins with 21 X 21 (441). 169, 676, 2704, 10816, 43264, 173056, 692224, 2768896, n 225, 900, 3600, 14400, 57600, 230400, 921600, 3686400, n 289, 1156, 4624, 18496, 73984, 295936, 1183744, 4734976, n 361, 1444, 5776, 23104, 92416, 369664, 1478656, 5914624, n No go; therefore, I am veering. This is also territory I have explored, but that was elsewhere in years behind. Want to take another look. After my look, I had to revise a note on entry 18 and add a note. Offline I have 15 pages which were once at ThirdAge relating to these probings. They are evidence of the progression of my thinking, thinking which began with a book I wrote but never officially published:Meanderings of an Amateur Mathematician.Number Theory Investigationsis the title for those pages. I know those pages were copied by at least one person, and may have been copied by more than one. This means they may still be out and about. Since I think in transit, and am not a professional mathematician, I can't vouch for their accuracy. However, I do hope anyone who has a copy used it to advantage. There's a chance that one day I will place myN T Iback online. - 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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## Thursday, February 21, 2008

### sw00818math-4.and.squares

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