A102604 Numbers k such that ((2*k)^k - 1)/(2*k - 1) is prime.

2, 3, 7, 41, 43, 79, 421

Offset: 1

Author

Pierre CAMI, Jan 29 2005

Keywords

• more
• nonn

Comments

The next k in the sequence is > 4261, if it exists.

Note that (b^k - 1)/(b-1) is prime only if k is prime, so all the elements in this sequence must be primes. - Marco Bodrato (marco2007(AT)bodrato.it), Oct 31 2007

a(8) > 20000, if it exists. - Michael S. Branicky, Aug 12 2024

Examples

			(((2*2)^2) - 1)/(2*2 - 1) = 15/3 = 5 is prime so a(1)=2.
		

Crossrefs

Cf. A088790.

Programs

Mathematica

 Select[Prime[Range[100]],PrimeQ[((2#)^#-1)/(2#-1)]&] (* Harvey P. Dale, Mar 09 2022 *)

PARI

lista(nn) = {forprime(n = 2, nn, if (isprime(((2*n)^n-1)/(2*n-1)), print1(n, ", ")););} \\ Michel Marcus, Feb 05 2014