A Natural Prime-Generating Recurrence
Eric S. Rowland
Department of Mathematics
Piscataway, NJ 08854
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.
Full version: pdf,
(Concerned with sequences
Received July 1 2008;
revised version received July 20 2008.
Published in Journal of Integer Sequences, July 20 2008.
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