A201357 Numbers k such that (2^k + k + 1)*2^k - 1 is prime.

1, 13, 1468, 2701, 2959, 3735, 8686, 11920, 89757

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Example

13 is in the sequence because (2^13 + 13 + 1)*2^13 - 1 = 67223551 is prime.

Mathematica

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

Prog

(PARI) is(n)=isprime((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 12 2022

Crossrefs

Cf. A201356, A201358, A201359, A201360, A201361, A201362, A201363.

Sequence in context: A353030 A064962 A242562 * A220551 A185073 A185193

Adjacent sequences: A201354 A201355 A201356 * A201358 A201359 A201360

Keyword

nonn,hard,more

Author

Michel Lagneau, Nov 30 2011

Extensions

a(8) from Michael S. Branicky, Jan 12 2022

a(9) from Michael S. Branicky, Aug 14 2024

Status

approved