Bounds for the 3x+1 Problem using Difference Inequalities
Number Theory
2015-06-26 v1 Dynamical Systems
Abstract
We study difference inequality systems for the 3x+1 problem introduced by the first author in 1989. These systemes can be used to give lower bounds for the number of integers below x that contain 1 in their forward orbit under the 3x+1 map. Previous methods gave away some information in these inequalities. We give an improvement which apparantly extracts full information from the inequalities. By computer aided proof we show that at least x^{0.84} of the integers below x contain 1 in their forward orbit under the 3x+1 map.
Cite
@article{arxiv.math/0205002,
title = {Bounds for the 3x+1 Problem using Difference Inequalities},
author = {Ilia Krasikov and Jeffrey C. Lagarias},
journal= {arXiv preprint arXiv:math/0205002},
year = {2015}
}
Comments
21 pages latex, 3 figures