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%I #25 May 17 2014 02:52:08
%S 2,4,5,6,10,13
%N Numbers n such that n^k - (n-1)^k - ... - 3^k - 2^k - 1 is prime for some k.
%C a(7) > 13. See A240747 for more information.
%C a(n) is also the n-values such that A240747(n) is nonzero.
%C It is known that a(n) == 1 mod 4 or 2 mod 4 (except a(2) = 4).
%C If n is not squarefree, then n is not a member of this sequence.
%C It is known that 17, 22, 30, 41, 66, and 194 are members of this sequence.
%e There are primes of the form 2^k-1 (A000043) so 2 is a member of this sequence.
%o (PARI) s(n) = for(k=1,6000,if(ispseudoprime(n^k-sum(i=1,n-1,i^k)),return(k)))
%o n=1; while(n<200,if(s(n),print(n));n+=1)
%Y Cf. A000043, A240747, A240507, A240503.
%K nonn,more,hard
%O 1,1
%A _Derek Orr_, Apr 11 2014
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