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If M(n) is the n-th Mersenne prime, then a(n) is the smallest positive integer such that 2*a(n)*M(n)*M(n+1)-1 is prime.
1

%I #7 Mar 21 2015 01:36:25

%S 1,1,1,12,1,25,3,13,7,153,43,423,52,916,136,1111,1270,442,2737,975

%N If M(n) is the n-th Mersenne prime, then a(n) is the smallest positive integer such that 2*a(n)*M(n)*M(n+1)-1 is prime.

%C a(21) > 4200. - _Robert G. Wilson v_

%C a(21) > 12000, a(22)=6669, a(23) > 10000, a(24)=5970. - _Ray G. Opao_, Apr 15 2004

%e a(4) = 12: 2(12)(2^7-1)(2^13-1)-1 = 24(127)(8191)-1 = 24966167, which is prime.

%t p = { (* the list of Mersenne exponents in A000043 *) }; f[n_] := Block[{k = 1, q = 2^p[[n]] - 1, r = 2^p[[n + 1]] - 1}, While[ !PrimeQ[2k*q*r - 1], k++ ]; k]; Do[ Print[ f[n]], {n, 25}] (* _Robert G. Wilson v_, Apr 10 2004 *)

%K nonn

%O 1,4

%A _Ray G. Opao_, Apr 08 2004