Infinite arithmetical progressions and global trees in natural numbers structure

Genady Ryabov, Vladimir Serov

Abstract


The article is a continuation of the natural numbers structure research on the basis of infinitary structures composition, infinite arithmetical progressions, global d-ary trees and the set of non-negative natural N. The semi-additive canonical form of natural number with the given module d is offered, on the basis of Euclid's algorithm. The definition of the global, directed 6-ary tree (GT) as a graph of nodes marking process by the sequence of natural numbers is given. The choice of the basic modules d for GT structure other than 6 is considered. It is noted also the "galactic" character of GT. The ring progression and the quasi-progression with a variable difference d, as a result of progressions merging are entered.

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References


Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao, "Long gaps between primes," arXiv:1412.5029v2 [math.NT], 6 Apr 2015. Available: http://arxiv.org/pdf/1412.5029v2

G. G. Ryabov, V. A. Serov, “On natural numbers structure on the basis of six arithmetical progressions,” International Journal of Open Information Technologies, 2016, vol. 4, no. 4, pp. 49–53. Available (in russian): http://injoit.org/index.php/j1/article/view/277

G. G. Ryabov, V. A. Serov, “Classification of natural numbers based on arithmetic progressions with a difference 6,” International Journal of Open Information Technologies, 2016, vol. 4, no. 12, pp. 13–15. Available: http://injoit.org/index.php/j1/article/view/355/314

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ISSN: 2307-8162