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Single Curio View: (Seek other curios for this number) Let a(1) = 7 and a(n) = a(n1) + gcd(n, a(n1)), for n>1. Here "gcd" means the greatest common divisor. Recently, Rutgers graduate student Eric Rowland proved that a(n)  a(n1) is either 1 or a prime! The differences begin 1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, .... It is not known if all odd primes occur in this list. Jonathan Sondow found that 587 is the smallest odd prime that does not appear in the first 10000 prime terms.
Submitted: 20080821 19:35:35; Last Modified: 20090302 20:05:30.
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