The Jacobsthal-Collatz-Terras model of conjecture the natural numbers in <i>κq</i> + 1 problems

Petro  Kosobutskyy

doi:10.59400/jam1767

The Jacobsthal-Collatz-Terras model of conjecture the natural numbers in κq + 1 problems

Petro Kosobutskyy Institute of Computer Science and Information Technologies, Lviv Polytechnic National University, 79013 Lviv, Ukraine

Article ID: 1767

DOI: https://doi.org/10.59400/jam1767

Keywords: recurrence Jacobsthal number; Terrase total stopping time; Collatz conjecture; natural numbers

Abstract

In the work, the unity of the model in both directions of the change of the power of two of the conjecture of natural numbers structured in the form of a set parametrized by a set of odd θ sequences θ × 2 n is justified for the first time. It is shown that the graphs of the direct n(tst) → ∞ and reverse n → 0 conjecture of numbers are correctly displayed by the branching diagram of the sequences oriented along the time axis of the full stop of Terrase. The distance between neighbouring nodes is shown to correlate with the Collatz function. The distance δm(p), κ = ακCκq±1 between adjacent nodes is shown to be correlated with the Collatz function. The obtained formula for calculating the period Tκ = ln2(1 + ακκ) according to the degree of formation of powers n. Based on the analysis of regularities of recurrent Jacobsthal numbers and Terras complete stop time, it is shown that the Collatz problem is a partial case of the general Jacobsthal-Collattz-Terrase model of the conjecture of numbers N in both directions of the change of the power of two. Based on this model, the formation of tst{q} sequences was established for numbers with the same lengths as the Collatz sequence CSq.

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Published

2025-03-17

How to Cite

Kosobutskyy, P. (2025). The Jacobsthal-Collatz-Terras model of conjecture the natural numbers in κq + 1 problems. Journal of AppliedMath, 3(2), 1767. https://doi.org/10.59400/jam1767

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