A natural prime-generating recurrence

dc.creatorRowland, Eric S.
dc.date2007-10-17
dc.date2008-07-23
dc.date.accessioned2026-07-07T09:51:56Z
dc.date.available2026-07-07T09:51:56Z
dc.descriptionFor 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.description11 pages, 2 figures; published version
dc.identifierhttps://arxiv.org/abs/0710.3217
dc.identifierhttp://arxiv.org/abs/0710.3217
dc.identifierJournal of Integer Sequences 11 (2008) 08.2.8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165420
dc.subjectNumber Theory
dc.subject11A41, 11B37, 11A05
dc.titleA natural prime-generating recurrence
dc.typetext

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