A Natural PrimeGenerating Recurrence
Abstract
For the sequence defined by a(n) = a(n1) + gcd(n,a(n1)) with a(1) = 7 we prove that a(n)  a(n1) takes on only 1's 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.
 Publication:

Journal of Integer Sequences
 Pub Date:
 July 2008
 arXiv:
 arXiv:0710.3217
 Bibcode:
 2008JIntS..11...28R
 Keywords:

 Mathematics  Number Theory;
 11A41;
 11B37;
 11A05
 EPrint:
 11 pages, 2 figures