A natural prime-generating recurrence
Number Theory
2008-07-23 v3
Abstract
For the sequence defined by a(n) = a(n-1) + gcd(n, a(n-1)) with a(1) = 7 we prove that a(n) - a(n-1) takes on only 1s and primes, making this recurrence a rare "naturally occurring" generator of primes. Toward a generalization of this result to an arbitrary initial condition, we also study the limiting behavior of a(n)/n and a transience property of the evolution.
Cite
@article{arxiv.0710.3217,
title = {A natural prime-generating recurrence},
author = {Eric S. Rowland},
journal= {arXiv preprint arXiv:0710.3217},
year = {2008}
}
Comments
11 pages, 2 figures; published version