Preprint on ResearchGate.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: We study a natural extension of the Collatz mapping to two variables and present a variety of analytic and experimental results, including identities satisfied by cycles of this mapping, the discovery of non-trivial cycles, the observation of divergent trajectories, and an apparent relationship to Benford’s law. Most interestingly, we observe that every cycle corresponds to a semi-convergent of the continued fraction expansion of 1 − 1/ log2(3) in the sense that the ratio of the number of strictly even terms to the length of the cycle is such a semi-convergent.
Bibtex:
@misc{,
author = {Erin T. Albertin and Zachary P. Bradshaw and Anthony Nguyen},
title = {On a Lattice Collatz Function with Nontrivial Cycles},
year = {2025},
url = {https://www.researchgate.net/profile/Zachary-Bradshaw-2/publication/391700765_On_a_Lattice_Collatz_Function_with_Nontrivial_Cycles/links/6823571d8a76251f22e16363/On-a-Lattice-Collatz-Function-with-Nontrivial-Cycles.pdf},
}
Reference Type: Preprint
Subject Area(s): Analysis, Number Theory