A130536 Prime numbers arising from A057856.

3, 5, 7, 41, 11, 13, 113, 17, 19, 2211377674535255285545615254209921, 23, 313, 66977, 29, 31, 149057, 613, 37, 761, 41, 43, 1013, 47, 1201, 1301, 53, 1146097

Offset: 1

Author

Tomas Xordan, Jun 02 2007

Keywords

• nonn
• hard

Comments

Conjecture: For all pairs of relative prime numbers (x, y) there exists at least one number n = 2^m and one prime number p such that p = x^n + y^n. This sequence shows one case of this conjecture where y = x + 1.

Examples

			a(10)=2211377674535255285545615254209921 because A057856(10)=32 and 2211377674535255285545615254209921 = 10^32 + 11^32 = 100000000000000000000000000000000 + 2111377674535255285545615254209921.
		

Crossrefs

Cf. A057856.

Programs

PARI

a(n) = my(k=1); while (!isprime(p=(n+1)^k + n^k), k++); p; \\ Michel Marcus, Sep 16 2018