A Conjecture on the Collatz-Kakutani Path Length for the Mersenne Primes
Number Theory
2012-08-06 v3
Abstract
We present here a new conjecture for the nature of the Mersenne prime numbers by connecting it with the Collatz-Kakutani problem. By introducing a natural path length on the basis of the Collatz-Kakutani tree, we conjecture that this path length of a Mersenne prime from the root of the Collatz-Kakutani tree is approximately proportional to the index of the Mersenne prime. We also discuss difference of behaviors between Mersenne numbers and Mersenne primes.
Cite
@article{arxiv.1104.2804,
title = {A Conjecture on the Collatz-Kakutani Path Length for the Mersenne Primes},
author = {Toru Ohira and Hiroshi Watanabe},
journal= {arXiv preprint arXiv:1104.2804},
year = {2012}
}
Comments
10 pages, 4 figures, submitted for a publication