A natural prime-generating recurrence

Details A natural prime-generating recurrence A natural prime-generating recurrence

2007-10-17

arxiv.org/abs/0710.3217v3

Journal of Integer Sequences 11 (2008) 08.2.8

Mathematics

Number Theory

11 pages, 2 figures; published version

Scientific paper

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.

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