%I A115596
%S A115596 2,2,2,7,2,3,3,5,2,2,5,3,2,37,2,17,3,61,23,7,2,2,7,5,7,59,5,2,59,2,59,
               3,
%T A115596 47,2,2,43,2,3,5,31,19,7,3,5,2,2,2,37,13,17,3,2,3,2,3,7,5,79,3,7,3,2,5,
%U A115596 5,7,7,53,2,67,2,7,79,2,5,3,5,29,17,3,37,2,3,2,3,43,3,3,3,13,3,2,5,3,5
%N A115596 The least number a(n)=k>1 such that (p+1)^k - p^k is prime, p = n-th 
               prime.
%C A115596 Values k=1 is omitted as in this case p is Sophie Germain prime (2p+1 
               is also prime) A005384.
%F A115596 p=n-th prime, (p+1)^k - p^k is prime, k>1 is minimal.
%e A115596 a(1)=2 because (2+1)^2-2^2=5 is prime;
%e A115596 a(14)=37 because p(14)=43 and
%e A115596 (43+1)^37-43^37=3679488080703419029992001830200360494989758810080014618823621
%e A115596 is prime.
%t A115596 s={};Do[n=Prime[i];Do[If[PrimeQ[(n+1)^k-n^k],AppendTo[s,k];Goto[ne]],
               {k,2,100}];Label[ne],{i,300}];s
%Y A115596 Cf. A005384.
%Y A115596 Sequence in context: A129365 A021453 A053789 this_sequence A029610 A094246 
               A023573
%Y A115596 Adjacent sequences: A115593 A115594 A115595 this_sequence A115597 A115598 
               A115599
%K A115596 nonn
%O A115596 1,1
%A A115596 Zak Seidov (zakseidov(AT)yahoo.com), Jan 25 2006