A201359 Numbers k such that (2^k + k - 1)*2^k - 1 is prime.

1, 2, 3, 5, 9, 18, 30, 48, 54, 278, 450, 464, 1425, 1428, 3029, 7314, 14273, 15399, 36962, 50369

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Example

3 is in the sequence because (2^3 + 3 - 1)*2^3 - 1 = 79 is prime.

Mathematica

lst={}; Do[If[PrimeQ[(2^n + n-1)*2^n-1], AppendTo[lst, n]], {n, 10000}]; lst
Select[Range[7320], PrimeQ[(2^#+#-1)2^#-1]&] (* Harvey P. Dale, Feb 13 2021 *)

Prog

(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 12 2022

Crossrefs

Cf. A201356, A201357, A201358, A201360, A201361, A201362, A201363.

Sequence in context: A320641 A365640 A047021 * A369392 A047031 A056766

Adjacent sequences: A201356 A201357 A201358 * A201360 A201361 A201362

Keyword

nonn,hard,more

Author

Michel Lagneau, Nov 30 2011

Extensions

a(17)-a(18) from Michael S. Branicky, Jan 12 2022

a(19)-a(20) from Michael S. Branicky, Apr 10 2023

Status

approved