A087038 Smallest integer x > 1 such that x^x + n is prime, or 0 if no such x exists.

2, 3, 2, 3, 444

Offset: 1

Author

Hugo Pfoertner, Jul 31 2003

Keywords

• nonn
• more

Comments

The sequence with the unknown terms indicated by ?: 2, 3, 2, 3, 444, ?, 2, ?, 2, 3, ?, 5, 2, 3, 2, 3, ?, 19, 2, 3, 4, 19, 6, ?, 2, 3, 2, 15, 30, 7, 6, 3, 2, 3, 6, ?, 2, 5, 2, 3, ...

The unknown terms a(6), a(8), a(11), a(17), a(24), a(36) are > 6000.

It is conjectured that such x always exists. - Dean Hickerson

We can show that for all n=(6k-1)^3, k > 0, there is no such x, which disproves the conjecture. See the main entry A087037 for more details. - Farideh Firoozbakht and M. F. Hasler, Nov 27 2009

Examples

			a(4)=3 because 3^3 + 4 = 27 + 4 = 31 is prime.
		

Links

• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A000312 (n^n), A087037 (x^x+n is prime, x>0).

Extensions

Name edited by Altug Alkan, Apr 01 2018