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

1, 2, 13, 72, 318, 13583

Offset

1,2

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

Links

Table of n, a(n) for n=1..6.

Example

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).

Prog

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

Crossrefs

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

Sequence in context: A289926 A188676 A330499 * A289790 A109112 A163190

Adjacent sequences: A097346 A097347 A097348 * A097350 A097351 A097352

Keyword

more,nonn

Author

Rick L. Shepherd, Aug 07 2004

Extensions

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

Status

approved