A122900 Minimum prime of the form n^k + (n+1)^k for k>1, or 0 if no such prime exists.

5, 13, 337, 41, 61, 3697, 113, 10657, 181, 2211377674535255285545615254209921

Offset: 1

Author

Alexander Adamchuk, Sep 18 2006

Keywords

• hard
• nonn

Comments

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.

All nonzero a(n) have a form n^(2^m) + (n+1)^(2^m).

The exponents m are listed in A080121. The first occurrence of each exponent m in A080121 is listed in A122902.

Examples

			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.
		

Crossrefs

Cf. A077659, A080121, A122902, A080208.

Extensions

Edited by Max Alekseyev, Sep 09 2020