The power transformation of Newton's binomial forms two equal 3n±1 algorithms for transformations of numbers n belongs to N, each of which have one infinite cycle with a unit lower limit of oscillations. It is shown that in the reverse direction, the Kollatz sequence is formed by the lower limits of the corresponding cycles, and the last element goes to a multiple of three odd numbers.
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 Kmain and side m >1 graphs and their corresponding sequences {Kmain } and {Km } are related by the relation {Km }=m⋅{Kmain }. 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.