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%I #12 Jun 27 2021 11:54:44
%S 1,1,2,1,1,2,1,2,1,5
%N a(n) is the smallest k > 0 such that n^2^k + (n+1)^2^k is prime, or -1 if no such k exists.
%C This sequence is the base-2 logarithm of A077659. It is known that a(11) > 22. Is it possible that 11^2^k + 12^2^k is composite for all k > 0?
%C The corresponding primes are listed in A122900. Currently a(n) is unknown for n in {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 0 < k < 10 are checked. The first occurrence of each exponent k is listed in A122902. - _Alexander Adamchuk_, Sep 18 2006
%H T. D. Noe, <a href="http://www.sspectra.com/math/GenFermat11.txt">Factorizations of Generalized Fermat Numbers 12^2^k + 11^2^k</a>
%F If A058064(n) > 0, then a(n) = A058064(n). - _Max Alekseyev_, Sep 10 2020
%Y Cf. A058064, A057856, A077659, A122900, A122902.
%K hard,more,nonn
%O 1,3
%A _T. D. Noe_, Jan 29 2003
%E Edited by _Max Alekseyev_, Sep 09 2020
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