A201358 Numbers k such that (2^k + k - 1)*2^k + 1 is prime.

1, 5, 49, 269, 2387, 2945, 5897, 11929, 30433

Offset

1,2

Links

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

Example

5 is in the sequence because (2^5 + 5 - 1)*2^5 + 1 = 1153 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(3000) # Michael S. Branicky, Jan 11 2022

Crossrefs

Cf. A201356, A201357, A201359, A201360, A201361, A201362, A201363.

Sequence in context: A058927 A083224 A352371 * A242035 A093188 A218421

Adjacent sequences: A201355 A201356 A201357 * A201359 A201360 A201361

Keyword

nonn,hard,more

Author

Michel Lagneau, Nov 30 2011

Extensions

a(8) from Michael S. Branicky, Jan 11 2022

a(9) from Michael S. Branicky, Apr 09 2023

Status

approved