A256594 - OEIS

%I #28 Sep 08 2022 08:46:11

%S 0,1,259,16708,18655,26304,61999,110251

%N Numbers k such that k!*2^k + 1 is prime.

%F a(n) = A080778(n+1)/2 for n >= 2. - _Amiram Eldar_, Dec 06 2018

%e 0 is in the sequence since 0!*2^0 + 1 = 2 is prime.

%t Select[Range[0, 20000], PrimeQ[2^#*#! + 1] &]

%o (Magma) [n: n in [0..3*10^2] | IsPrime(Factorial(n)*2^n+1)]; // _Vincenzo Librandi_, Apr 05 2015

%o (PARI) for(n=0,300,if(ispseudoprime(n!*2^n+1),print1(n,", "))) \\ _Derek Orr_, Apr 05 2015

%o (Python)

%o from sympy import factorial, isprime

%o for n in range(0,300):

%o     if isprime(factorial(n)*(2**n)+1):

%o         print(n, end=', ') # _Stefano Spezia_, Dec 06 2018

%Y Cf. A007749, A080778, A117141, A091415.

%K nonn,hard,more

%O 1,3

%A _Robert Price_, Apr 03 2015

%E a(6)-a(8), from the data at A080778, added by _Amiram Eldar_, Dec 06 2018