A Natural Prime-generating Recurrence
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چکیده
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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تاریخ انتشار 2008