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%I #30 Oct 12 2018 04:42:51
%S 2,2,2,7,2,3,3,5,2,2,5,3,2,37,58543,2,4663,17,3,61,23,7,2,2,7,5,7,59,
%T 5,2,59,2,196873
%N The least number k > 1 such that (p+1)^k - p^k is prime, p = n-th prime.
%C Values k=1 is omitted as in this case p is Sophie Germain prime (2p+1 is also prime) A005384.
%C Each term is necessarily prime. Sophie Germain primes correspond to case k = 2. - _Giuseppe Coppoletta_, Oct 10 2018
%e a(1)=2 because (2+1)^2-2^2 = 5 is prime;
%e a(14)=37 because p(14)=43 and (43+1)^37-43^37 = 3679488080703419029992001830200360494989758810080014618823621 is prime.
%t s={}; Do[n=Prime[i];k=2; While[!PrimeQ[(n+1)^k-n^k],k++]; AppendTo[s, k], {i, 14}]; s (* _Amiram Eldar_, Oct 12 2018 *)
%o (PARI) a(n)=my(p=prime(n),k=1); while(!ispseudoprime((p+1)^k++-p^k),); k \\ _Charles R Greathouse IV_, Oct 08 2013
%Y Cf. A005384, A058013.
%K nonn,more
%O 1,1
%A _Zak Seidov_, Jan 25 2006
%E Edited by _Giuseppe Coppoletta_, Oct 10 2018
%E a(15)-a(33) from _Vaclav Kotesovec_, Oct 11 2018
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