2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165420For 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.11 pages, 2 figures; published versionNumber Theory11A41, 11B37, 11A05text