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(another Prime Pages' Curiosity)
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Let a(1) = 7 and a(n) = a(n-1) + gcd(n, a(n-1)), for n>1. Here "gcd" means the greatest common divisor. Recently, Rutgers graduate student Eric Rowland proved that a(n) - a(n-1) 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: 2008-08-21 19:35:35;   Last Modified: 2009-03-02 20:05:30.



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