Classification of natural numbers based on arithmetic progressions with a difference 6.

Gennady Ryabov, Vladimir Serov

Abstract


The article considers a classification of natural numbers based on the submission of the set of all natural numbers as union of six infinite arithmetic progressions. The classes themselves (bijective to the progressions) are considered as members of two finite semigroups with regard to the operations of addition and multiplication. The binary relations between classes and examples of natural numbers properties at such classification  are given.

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References


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, “Composition of Infinitary Structures,” Numerical methods and programming, 2015, vol. 16, pp. 557-565. Available (in russian): http://num-meth.srcc.msu.ru/zhurnal/tom_2015/pdf/v16r452.pdf

G. G. Ryabov, V. A. Serov, “On composition of infinitary structures and symmetries between primes,” International Journal of Open Information Technologies, 2015, vol. 3, no. 12, pp. 4–6. Available: http://injoit.org/index.php/j1/article/view/248/197


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