A162487 Values of y for A094133: primes of the form x^y + y^x, x > y > 1.

2, 2, 2, 2, 2, 5, 3, 15, 7, 33, 8, 9, 21, 34, 9, 56, 80, 32, 67, 97, 65, 45, 36, 133, 98, 51, 9, 76, 20, 8, 157, 87, 200, 214, 2, 20, 91, 2, 111, 122, 5, 247, 142, 56, 98, 342, 184, 289, 21, 364, 32, 2, 365, 423, 34, 91, 157, 329, 441, 234, 234, 98, 87, 291, 513

Offset: 1

Author

M. F. Hasler, Jul 04 2009

Keywords

• nonn

Comments

See A094133 for links, references and more information.

Whereas a list of the possible x-values can be established by a brute-force search, this is not possible for the y-values. Some, however, may easily be excluded. For example, 4 cannot occur in this sequence, since for even y, x must be odd, and for x = 2k - 1, x^4 + 4^x = (x^2 + 2^k*x + 2^x)(x^2 - 2^k*x + 2^x).

Formula

A094133(n) = A162486(n)^A162487(n) + A162487(n)^A162486(n).

Extensions

More terms from Jinyuan Wang, Mar 03 2020