1,2

a(8) = 86, a(9) = 59. Minimum primes of the form n^(2^m) + (n+1)^(2^m) are listed in A122900[n] = {5, 13, 337, 41, 61, 3697, 113, 10657, 181, 2211377674535255285545615254209921, ...}. The exponents m(n) are listed in A122901[n] = { 1, 1, 2, 1, 1, 2, 1, 2, 1, 5, 0, 1, 2, 1, 0, 2, 1, 0, 1, 0, 4, 1, 3, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 4, 1, 2, 0, 4, 0, 1, 2, 0, 1, 0, 0, 0, 2, 0, 4, 0, 0, 9, 1, 0, 0, 2, 0, 1, 3, 2, 2, 1, 1, 0, 1, 0, 2, 4, 3, 0, 2, 1, 4, 0, 1, 0, 1, 1, 8, 1, 2, 2, 1, 0, 0, 4, 0, 6, 4, 1, 2, 1, 1, ...}.

a(7) = 255. a(10)-a(13)>1000, a(14)-a(16)>100.

T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m

Eric Weisstein's World of Mathematics, Generalized Fermat Number

A122901[n] begins {1,1,2,1,1,2,1,2,1,5,0,1,2,1,0,2,1,0,1,0,4,1,3,1,...}.

So a(1) = 1, a(2) = 3, a(3) = 23, a(4) = 21, a(5) = 10.

Cf. A122900, A122901.

Cf. A080208, A078902, A080134.

Adjacent sequences: A122899 A122900 A122901 this_sequence A122903 A122904 A122905

Sequence in context: A088605 A063562 A130475 this_sequence A124076 A103361 A136090

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 18 2006, Oct 01 2006