English

Stochastic Models for the 3x+1 and 5x+1 Problems

Number Theory 2011-06-22 v1

Abstract

This paper discusses stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1 problem. The stochastic models are rigorously analyzable, and yield heuristic predictions (conjectures) for the behavior of 3x+1 orbits and 5x+1 orbits.

Keywords

Cite

@article{arxiv.0910.1944,
  title  = {Stochastic Models for the 3x+1 and 5x+1 Problems},
  author = {Alex V. Kontorovich and Jeffrey C. Lagarias},
  journal= {arXiv preprint arXiv:0910.1944},
  year   = {2011}
}

Comments

68 pages, 9 figures, 4 tables

R2 v1 2026-06-21T13:56:46.251Z