1,1

Currently a(n) = 1 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 are checked. All a(n) that are not equal to 1 have a form n^(2^m) + (n+1)^(2^m). 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,...}. The first occurrence of exponent m>0 in A122901[n] is listed in A122902[m] ={1,3,23,21,10,95,...}.

a(1) = 5 because 1^2 + 2^2 = 5 is prime.

a(2) = 13 because 2^2 + 3^2 = 13 is prime.

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.

a(11) = 1 because prime of the form 11^k + 12^k is not found for 1<k<2000.

Cf. A122901, A122902, A080208.

Sequence in context: A124878 A085554 A067135 this_sequence A145557 A012033 A007540

Adjacent sequences: A122897 A122898 A122899 this_sequence A122901 A122902 A122903

hard,nonn

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