Infinite arithmetical progressions and global trees in natural numbers structure

Genady Ryabov, Vladimir Serov


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

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):

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:

I.M. Vinogradov, Osnovy teorii chisel. M.: Nauka, 1972.


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