Boris B. Stefanov
2021-03-17
<p>This paper proposes a new two-parameter generalization T_{b,s}(x) of the Z -> Z Collatz function T(x) and restates the eponymous conjecture in terms of the proposed function. The generalization obviates some of the conditions for emergence of terminal cycles for the Collatz T(x) function over the integers. The stopping behavior of the T_{b,s}(x) is qualitatively similar to that of the T(x). The paper presents theoretical discussion of the generalization and computational results on the terminal cycles and stopping times of T_{b,s}(x). The {1,2} cycle of T(x) is shown to be a case of coincidence of three independent cycle categories of T_{b,s}(x).</p>
https://doi.org/10.5281/zenodo.4609709
oai:zenodo.org:4609709
eng
Zenodo
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.4609708
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 03(01), 19–25, (2021-03-17)
Collatz conjecture
3x+1 problem
iteration
convergence
terminal cycles
Two-Parameter Generalization of the Collatz Function: Characterization of Terminal Cycles and Empirical Results
info:eu-repo/semantics/article