A268692 Numbers k such that 2^(k-1)*(2^k - 1) + 1 is prime (see A134169).

1, 2, 3, 6, 9, 10, 13, 19, 45, 46, 58, 141, 271, 336, 562, 601, 1128, 1635, 2718, 2920, 3933, 4351, 4729, 6556, 8349, 10851, 32641, 34039, 41050, 63732, 64738, 68173, 88690

Offset: 1

Author

Jeppe Stig Nielsen, Feb 11 2016

Keywords

• nonn
• more

Comments

The intersection of this sequence with A000043 gives 2, 3, 13, 19, ... which are the indices corresponding to primes just next to perfect numbers (A000396), see A061644.

There are prime members of this sequence (271, 601, 4729, ...) which are not in A000043.

a(30) > 50000. All the primes corresponding to terms up to a(29) have been certified by the PFGW software performing the Brillhart-Lehmer-Selfridge N-1 test. - Giovanni Resta, Apr 11 2016

a(30)-a(32) terms have been certified by the PFGW software performing the Brillhart-Lehmer-Selfridge N-1 test. - Jorge Coveiro, Oct 29 2023

a(33) term has been certified by the PFGW software performing the Brillhart-Lehmer-Selfridge N-1 test. - Jorge Coveiro, Mar 08 2024

Crossrefs

Cf. A134169, A061644, A000043, A000396, A006516.

Programs

PARI

for(n=0,10^5,ispseudoprime(2^(n-1)*(2^n-1)+1) && print1(n,", "))

Extensions

a(27)-a(29) from Giovanni Resta, Apr 11 2016

a(30)-a(32) from Jorge Coveiro, Oct 29 2023

a(33) from Jorge Coveiro, Mar 08 2024