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  4. RECURRENCE AND STRUCTURING OF SEQUENCES OF TRANSFORMATIONS 3N + 1 AS ARGUMENTS FOR CONFIRMATION OF THE СOLLATZ HYPOTHESIS

RECURRENCE AND STRUCTURING OF SEQUENCES OF TRANSFORMATIONS 3N + 1 AS ARGUMENTS FOR CONFIRMATION OF THE СOLLATZ HYPOTHESIS

CDS.
2023;
Volume 5, Number 1
: 28-33
https://doi.org/10.23939/cds2023.01.028
Received: July 10, 2023
Revised: August 28, 2023
Accepted: September 28, 2023
Authors:
  1. Petro Kosobutskyy
  2. Volodymyr Karkulovskyy
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

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.

Collatz conjecture
recurrent sequence
transformation 3n + 1
natural numbers

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