Additive Collatz Trajectories
Abstract
Collatz Conjecture (also known as Ulam's conjecture and 3x+1 problem) concerns the behavior of the iterates of a particular function on natural numbers. A number of generalizations of the conjecture have been subjected to extensive study. This paper explores Additive Collatz Trajectories, a particular case of a generalization of Collatz conjecture and puts forward a sufficient and necessary condition for looping of Additive Collatz Trajectories, along with two minor results. An algorithm to compute the number of equivalence classes when natural numbers are quotiented by the limiting behavior of their corresponding trajectories is also proposed.
Cite
@article{arxiv.1611.03919,
title = {Additive Collatz Trajectories},
author = {Aalok Thakkar and Mrunmay Jagadale},
journal= {arXiv preprint arXiv:1611.03919},
year = {2016}
}
Comments
The 29th International Conference of The Jangjeon Mathematical Society on Number Theory and Special Functions and its Applications (ICJMSNTSFA'2016)