A157200 Numbers k such that k*(2k)^k - 1 is a prime.

2, 3, 6, 7, 12, 21, 113, 404, 735, 1944, 4973, 17459

Offset

1,1

Comments

Conjecture: there are infinitely many such primes.

a(12) > 10000. - Donovan Johnson, Aug 31 2010

Links

Table of n, a(n) for n=1..12.

Example

2*(2*2)^2 - 1 = 31 is prime, so 2 is a term;
3^(2*3)^2 - 1 = 107 is prime, so 3 is a term.

Mathematica

Do[cp=n*(2*n)^n-1; If[PrimeQ[cp], Print[n]], {n, 1, 2000}] (* generates the first 10 terms *)

Prog

(PARI) is(n)=ispseudoprime(n*(2*n)^n-1) \\ Charles R Greathouse IV, Jun 17 2013

Crossrefs

Sequence in context: A144120 A375401 A073712 * A255940 A167415 A354361

Adjacent sequences: A157197 A157198 A157199 * A157201 A157202 A157203

Keyword

hard,nice,nonn,more

Author

Lei Zhou, Feb 25 2009

Extensions

a(11) from Donovan Johnson, Aug 31 2010

a(12) from Michael S. Branicky, Aug 31 2024

Status

approved