%I #4 Mar 30 2012 17:36:43
%S 1,2,13,72,318,13583
%N Numbers n such that (Sum (2k)^k, k=1..n) + 1 is prime.
%C Some of the larger entries may only correspond to probable primes.
%C The numbers produced by 72 and 318 have now been certified prime by Primo. 13583, found by PrimeForm using recurrence mode, corresponds to a 60228-digit probable prime. - _Rick L. Shepherd_, Apr 29 2006
%e 13 is a term as 2^1 + 4^2 + 6^3 + 8^4 + 10^5 + 12^6 + 14^7 + 16^8 + 18^9 + 20^10 + 22^11 + 24^12 + 26^13 + 1 = 2518267981703965963, which is prime (certified with Primo).
%o (PARI) s=1; for(k=1,700, s=s+(2*k)^k; if(isprime(s), print1(k,",")))
%Y Cf. A073825 (Sum k^k, k=1..n, is prime), A097350 ((Sum (2k)^k, k=1..n) - 1 is prime).
%K more,nonn
%O 1,2
%A _Rick L. Shepherd_, Aug 07 2004
%E One more term from _Rick L. Shepherd_, Apr 29 2006
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