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A201361
Numbers k such that (2^k - k + 1)*2^k - 1 is prime.
7
1, 2, 3, 8, 14, 35, 75, 83, 89, 90, 215, 342, 753, 1452, 4578, 10337, 25580, 26381
OFFSET
1,2
EXAMPLE
3 is in the sequence because (2^3 - 3 + 1)*2^3 - 1 = 47 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(1500) # Michael S. Branicky, Jan 11 2022
KEYWORD
nonn,hard,more
AUTHOR
Michel Lagneau, Nov 30 2011
EXTENSIONS
a(16) from Michael S. Branicky, Jan 11 2022
a(17)-a(18) from Michael S. Branicky, Apr 07 2023
STATUS
approved