A282352 - OEIS

%I #17 Feb 15 2017 09:38:37

%S 2,3,3,3,3,3389,63559

%N Smallest value of x + y such that x^(2^k) + y^(2^k) is prime for every k = 0..n, where x > y are nonnegative integers.

%e a(0) = 2 because 2^(2^0) + 0^(2^0) = 2.

%e a(1) = 3 because 2^(2^0) + 1^(2^0) = 3 and 2^(2^1) + 1^(2^1) = 5 are prime.

%e a(2) = 3 because 2^(2^0) + 1^(2^0) = 3, 2^(2^1) + 1^(2^1) = 5, and 2^(2^2) + 1^(2^2) = 17 are prime.

%e a(n)     x       y

%e -----  -----   -----

%e 2        2       0

%e 3        2       1

%e 3        2       1

%e 3        2       1

%e 3        2       1

%e 3389     2669    720

%e 63559    34559   29000

%Y Cf. A111635.

%K nonn,more

%O 0,1

%A _Altug Alkan_, Feb 12 2017

%E a(6) from _Max Alekseyev_, Feb 14 2017