This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115596 #30 Oct 12 2018 04:42:51
%S A115596 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 A115596 5,2,59,2,196873
%N A115596 The least number 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.
%C A115596 Each term is necessarily prime. Sophie Germain primes correspond to case k = 2. - _Giuseppe Coppoletta_, Oct 10 2018
%e A115596 a(1)=2 because (2+1)^2-2^2 = 5 is prime;
%e A115596 a(14)=37 because p(14)=43 and (43+1)^37-43^37 = 3679488080703419029992001830200360494989758810080014618823621 is prime.
%t A115596 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 A115596 (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 A115596 Cf. A005384, A058013.
%K A115596 nonn,more
%O A115596 1,1
%A A115596 _Zak Seidov_, Jan 25 2006
%E A115596 Edited by _Giuseppe Coppoletta_, Oct 10 2018
%E A115596 a(15)-a(33) from _Vaclav Kotesovec_, Oct 11 2018