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 A077659 #5 Mar 30 2012 17:22:26
%S A077659 2,2,4,2,2,4,2,4,2,32
%N A077659 a(n) = smallest k>1 such that the sum n^k + (n+1)^k is prime, or -1 if no such k exists.
%C A077659 Checking k up through 1024 suggests that the sequence may continue -1, 2, 4, 2, -1, 4, 2, -1, 2, -1, 16, 2, 8, 2, 2, 4, 4, -1, 2, 2, 4, 2, 4, 2, 2, 4, 4, 4, 2, ...
%C A077659 For any a>1 and b>1, a^k + b^k is composite for all odd k>1. Hence if n^k + (n+1)^k is prime then k must be a power of 2.
%C A077659 It is known that a(11) > 2^22. Is it possible that 11^2^m + 12^2^m is composite for all m > 0?
%H A077659 T. D. Noe, <a href="http://www.sspectra.com/math/GenFermat11.txt">Factorizations of Generalized Fermat Numbers 12^2^k + 11^2^k</a>
%e A077659 a(3)=4 because 3^2 + 4^2 = 25 is not prime, but 3^4 + 4^4 = 337 is prime.
%t A077659 lst={}; For[n=1, n<=100, n++, k=2; While[k<=2^10 && !PrimeQ[n^k+(n+1)^k], k=2*k]; If[k<=2^10, AppendTo[lst, k], AppendTo[lst, -1]]]; lst
%Y A077659 Cf. A078902.
%Y A077659 Cf. A080121.
%K A077659 hard,more,nonn
%O A077659 1,1
%A A077659 _T. D. Noe_, Nov 14 2002