A201356 Numbers k such that (2^k + k + 1)*2^k + 1 is prime.

2, 3, 4, 5, 15, 23, 53, 57, 75, 233, 464, 671, 1431, 2021, 5861, 6056, 9063, 14801, 22682

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Example

4 is in the sequence because (2^4 + 4 + 1)*2^4 + 1 = 337 is prime.

Mathematica

lst={}; Do[If[PrimeQ[(2^n + n+1)*2^n+1], AppendTo[lst, n]], {n, 10000}]; lst
Select[Range[9100], PrimeQ[(2^#+#+1)2^#+1]&] (* Harvey P. Dale, Dec 10 2011 *)

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(2100) # Michael S. Branicky, Jan 12 2022

Crossrefs

Cf. A201357, A201358, A201359, A201360, A201361, A201362, A201363.

Sequence in context: A171593 A227535 A096774 * A183528 A145029 A145030

Adjacent sequences: A201353 A201354 A201355 * A201357 A201358 A201359

Keyword

nonn,hard,more

Author

Michel Lagneau, Nov 30 2011

Extensions

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

a(19) from Michael S. Branicky, Apr 09 2023

Status

approved