перетворення 3n + 1

It is shown that: 1. The sequence {2⁰,2¹, 2², 2³, 2⁴, 2⁵, 2⁶, 2⁷,2⁸,...} that forms the main graph m=1 of Collatz is related to the power transformation of Newton's binomial (1+1)^ξ, ξ=0, 1, 2, 3,... 2. The main K_main and side m >1 graphs and their corresponding sequences {K_main } and {K_m } are related by the relation {K_m }=m⋅{K_main }. 3.

It is shown that infinites of the subsequence of odd numbers is not a counterargument of the violation of the Collatz hypothesis, but a universal characteristic of transformations of natural numbers by the 3n + 1 algorithm. A recurrent relationship is established between the parameters of the sequence of Collatz transformations of an arbitrary pair of natural numbers n and 2n.