%I #9 Jun 13 2021 08:52:34
%S 5,13,337,41,61,3697,113,10657,181,2211377674535255285545615254209921
%N Minimum prime of the form n^k + (n+1)^k for k>1, or 0 if no such prime exists.
%C Currently a(n) is unknown for n = {11, 15, 18, 20, 28, 44, 46, 49, 51, 52, 53, 55, 57, 58, 61, 62, 64, 71, 73, 77, 81, 83, 91, 92, 94, ...}. All n < 100 and 1 < k < 2^10 have been checked.
%C All nonzero a(n) have a form n^(2^m) + (n+1)^(2^m).
%C The exponents m are listed in A080121. The first occurrence of each exponent m in A080121 is listed in A122902.
%e a(1) = 5 because 1^2 + 2^2 = 5 is prime.
%e a(2) = 13 because 2^2 + 3^2 = 13 is prime.
%e a(3) = 337 because 3^4 + 4^4 = 337 is prime but 3^3 + 4^3 = 91 and 3^2 + 4^2 = 25 are composite.
%Y Cf. A077659, A080121, A122902, A080208.
%K hard,nonn
%O 1,1
%A _Alexander Adamchuk_, Sep 18 2006
%E Edited by _Max Alekseyev_, Sep 09 2020