A080121 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.

1, 1, 2, 1, 1, 2, 1, 2, 1, 5

Offset: 1

Author

T. D. Noe, Jan 29 2003

Keywords

• hard
• more
• nonn

Comments

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?

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

Links

• T. D. Noe, Factorizations of Generalized Fermat Numbers 12^2^k + 11^2^k

Crossrefs

Cf. A058064, A057856, A077659, A122900, A122902.

Formula

If A058064(n) > 0, then a(n) = A058064(n). - Max Alekseyev, Sep 10 2020

Extensions

Edited by Max Alekseyev, Sep 09 2020