A201361 Numbers k such that (2^k - k + 1)*2^k - 1 is prime.

1, 2, 3, 8, 14, 35, 75, 83, 89, 90, 215, 342, 753, 1452, 4578, 10337, 25580, 26381

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Example

3 is in the sequence because (2^3 - 3 + 1)*2^3 - 1 = 47 is prime.

Mathematica

lst={}; Do[If[PrimeQ[(2^n - n+1)*2^n-1], AppendTo[lst, n]], {n, 10000}]; lst

Prog

(PARI) is(n)=ispseudoprime((2^n-n+1)<<n-1) \\ Charles R Greathouse IV, Feb 17 2017
(Python)
from sympy import isprime
def afind(limit, startk=1):
    pow2 = 2**startk
    for k in range(startk, limit+1):
        if isprime((pow2 - k + 1)*pow2 - 1):
            print(k, end=", ")
        pow2 *= 2
afind(1500) # Michael S. Branicky, Jan 11 2022

Crossrefs

Cf. A201356, A201357, A201358, A201359, A201360, A201362, A201363.

Sequence in context: A328881 A298349 A298343 * A129700 A197466 A049344

Adjacent sequences: A201358 A201359 A201360 * A201362 A201363 A201364

Keyword

nonn,hard,more

Author

Michel Lagneau, Nov 30 2011

Extensions

a(16) from Michael S. Branicky, Jan 11 2022

a(17)-a(18) from Michael S. Branicky, Apr 07 2023

Status

approved