A natural prime-generating recurrence
| dc.creator | Rowland, Eric S. | |
| dc.date | 2007-10-17 | |
| dc.date | 2008-07-23 | |
| dc.date.accessioned | 2026-07-07T09:51:56Z | |
| dc.date.available | 2026-07-07T09:51:56Z | |
| dc.description | 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. | |
| dc.description | 11 pages, 2 figures; published version | |
| dc.identifier | https://arxiv.org/abs/0710.3217 | |
| dc.identifier | http://arxiv.org/abs/0710.3217 | |
| dc.identifier | Journal of Integer Sequences 11 (2008) 08.2.8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165420 | |
| dc.subject | Number Theory | |
| dc.subject | 11A41, 11B37, 11A05 | |
| dc.title | A natural prime-generating recurrence | |
| dc.type | text |