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A Natural Prime-Generating Recurrence
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Eric S. Rowland

Department of Mathematics

Rutgers University

Piscataway, NJ 08854

USA

**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 1's 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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(Concerned with sequences
A084662
A084663
A106108
A132199
A134162
A135506 and
A137613.)

Received July 1 2008;
revised version received July 20 2008.
Published in *Journal of Integer Sequences*, July 20 2008.

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