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arXiv · 0710.3217

A natural prime-generating recurrence

Eric S. Rowland
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Abstract

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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Eric S. Rowland. 2008-07-23. A natural prime-generating recurrence. https://arxiv.org/abs/0710.3217

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