OFFSET
1,1
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
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
a(20) from Michael S. Branicky, Aug 16 2024
STATUS
approved