A game with divisors and absolute differences of exponents
Number Theory
2014-11-06 v1
Abstract
In this work, we discuss a number game that develops in a manner similar to that on which Gilbreath's conjecture on iterated absolute differences between consecutive primes is formulated. In our case the action occurs at the exponent level and there, the evolution is reminiscent of that in a final Ducci game. We present features of the whole field of the game created by the successive generations, prove an analog of Gilbreath's conjecture, and raise some open questions.
Cite
@article{arxiv.1411.1334,
title = {A game with divisors and absolute differences of exponents},
author = {Cristian Cobeli and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:1411.1334},
year = {2014}
}
Comments
14 pages, 7 figures, 1 table