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arXiv:1104.2804math.NT

A Conjecture on the Collatz-Kakutani Path Length for the Mersenne Primes

Toru Ohira, Hiroshi Watanabe

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.

arXiv comments
10 pages, 4 figures, submitted for a publication
Journal reference
DOI
Subjects
math.NTNumber Theory

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  1. MU puzzle 2 comments

    • On a slight tangent, I recently read a paper on an interesting relationship between Collatz path length and Mersenne primes. "Our main finding to report is the fact that a path length of a Mersenne prime is approximately proportional to its index for large n, namely, D(Mn) ≈…

      IntermernetView on HNParent context

    • You can de-PDF anything on the arXiv by chopping off the .pdf suffix and changing the /pdf/ to /abs/. For example, https://arxiv.org/abs/1104.2804

      evanbView on HNParent context

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