The nnss: Natural Number Summation SequenceYesterday I found a site wheremodulois explained clearly enough so that I was finally able to understand the concept of it and how it is used. Also yesterday some new insights regarding the natural number summation sequence appeared in my consciousness. I am going to try to clearly present them along with my older insights, and I do not expect I will attempt to use modular arithmetic. - If one allows "0" (accepting it as a non-negative integer) to be the first term of the natural number sequence/ so that it is at term-position 1 in that sequence, one will get these results: 0 1 x 0 = 0 and 0 + 1 = 1 1 2 x .5 = 1 and 1 + 2 = 3 2 3 x 1 = 3 and 3 + 3 = 6 3 4 x 1.5 = 6 and 6 + 4 = 10 4 5 x 2 = 10 and 10 + 5 = 15 5 6 x 2.5 = 15 and 15 + 6 = 21 6 7 x 3 = 21 and 21 + 7 = 28 7 8 x 3.5 = 28 and 28 + 8 = 36 8 9 x 4 = 36 and 36 + 9 = 45 - The first number in each row is the natural number. The second number in each row is the term-position number. The third number in each row is the t-p # divided by 2, and then made less by .5. The fourth number in each row is the value of the nnss term at that term's position. The fifth number in each row is the value of the nnss term at that term's position. The sixth number in each row is the term-position number. The seventh number in each row is the value of the next greater nnss term. - - My approach to modular arithmetic has been to work around it. It is known that multiples of "8" are central to determining the odd squares. What I saw was that/ adding 1 to (8 times any number in the nnss) = an odd square so long as "0" is allowed to be the first term in the nnss. Example: 8 x 36 = 288 288 + 1 = 289 17 x 17 - Letting non-negative integer = natural number, I also saw that by dividing aterm positionin a (0, 1, 2, 3, 4, 5, 6, 7, 8, n) natural number sequence by 2, and then multiplying that quotient by the value of the non-negative integer at that position would net one the sum of the non-negative integers through the natural numberat that position. Example: 3/2 = 1.5 1.5 x 2 = 3(note: "3" is 2's term position.)# Further examples: If you divide any non-negative integer by 2, then minus .5 from that quotient, then multiply that remainder by the non-negative integer you have chosen, the resulting product will be the natural number summation sequence term for all the non-negative integers prior to the non-negative integer you have chosen. If after having divided your chosen non-negative integer by 2, you add .5 to that quotient and then multiply that sum by your chosen non-negative integer, the resulting product will be the natural number summation sequence term for all the non- negative integers including/ your chosen non- negative integer. Okay: - 100/2 = 50 50 - .5 = 49.5 100 x 49.5 = 4950 100/2 = 50 50 + .5 = 50.5 100 x 50.5 = 5050 101/2 = 50.5 50.5 - .5 = 50 101 x 50 = 5050 101/2 = 50.5 50.5 + .5 = 51 101 x 51 = 5151 - (The ghost of Gauss is in all of this.) # - Another point of interest is: 1 = 1 x 1 3 = 1 x 3 6 = 2 x 3 10 = 2 x 5 15 = 3 x 5 21 = 3 x 7 28 = 4 x 7 = 2 x 14 36 = 4 x 9 = 3 x 12 = 2 x 18 45 = 5 x 9 = 3 x 15 55 = 5 x 11 - 2006-11-11 - # - [ last modified: 2007-10-17 ] 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, November 9, 2006

### sw00017math-nnss

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