загальний час зупинки

The paper investigates the role of Jacobsthal recurrent numbers in forming statistical patterns within the model of the natural number hypothesis q ϵ ℕ in the general problem of the form κ⋅q±1, where κ=1,3,5,…. A novel model is proposed for structuring the set of natural numbers as sequences of the form θ⋅2ⁿ, where the parameter θ takes odd values 1,3,5,…, and n is a natural number starting from zero.

A new branching tree model has been proposed for the first time in the direction of increasing degree 2ⁿ (merging in the reverse direction), which coincides with the direction of increasing total stopping time. It has been shown that each time corresponds to a sequence of individual numbers n(tst)→∞, the volume of which increases with time. Thus, it is proven that each time corresponds to a finite number of Collatz sequences of the same length.