A097349 Numbers n such that (Sum (2k)^k, k=1..n) + 1 is prime.

1, 2, 13, 72, 318, 13583

Offset: 1

Author

Rick L. Shepherd, Aug 07 2004

Keywords

• more
• nonn

Comments

Some of the larger entries may only correspond to probable primes.

The numbers produced by 72 and 318 have now been certified prime by Primo. 13583, found by PrimeForm using recurrence mode, corresponds to a 60228-digit probable prime. - Rick L. Shepherd, Apr 29 2006

Examples

			13 is a term as 2^1 + 4^2 + 6^3 + 8^4 + 10^5 + 12^6 + 14^7 + 16^8 + 18^9 + 20^10 + 22^11 + 24^12 + 26^13 + 1 = 2518267981703965963, which is prime (certified with Primo).
		

Crossrefs

Cf. A073825 (Sum k^k, k=1..n, is prime), A097350 ((Sum (2k)^k, k=1..n) - 1 is prime).

Programs

PARI

s=1; for(k=1,700, s=s+(2*k)^k; if(isprime(s), print1(k,",")))

Extensions

One more term from Rick L. Shepherd, Apr 29 2006