A057912 Numbers k such that 3*2^k - 5 is prime.

2, 3, 4, 7, 9, 10, 13, 15, 25, 31, 34, 48, 52, 64, 109, 145, 162, 204, 207, 231, 271, 348, 444, 553, 559, 1504, 1708, 3048, 3970, 4423, 4668, 5737, 5877, 6130, 8584, 10663, 12517, 16591, 18450, 19362, 22291, 34468, 36637, 52212, 59040, 130279, 236511, 392260, 496411, 536868, 565024, 662703, 908005

Offset: 1

Author

Robert G. Wilson v, Nov 16 2000

Keywords

• nonn
• more

Comments

a(44) > 44233. - Jinyuan Wang, Feb 02 2020

a(54) > 1000000 - Jon Grantham, Jul 30 2023

Links

• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Crossrefs

Cf. A057913 (3*2^k + 5 is prime).

Cf. A048488 (3*2^k - 5, but with different offset).

Programs

Mathematica

Do[ If[ PrimeQ[ 3*2^n - 5 ], Print[ n ] ], {n, 1, 3000} ]

PARI

is(n)=ispseudoprime(3*2^n-5) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(36)-a(41) from Vincenzo Librandi, Oct 10 2013

a(42)-a(43) from Jinyuan Wang, Feb 02 2020

a(44)-a(45) from Michael S. Branicky, May 20 2023

a(46)-a(53) from Jon Grantham, Jul 30 2023