A256594 Numbers k such that k!*2^k + 1 is prime.

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

Offset: 1

Author

Robert Price, Apr 03 2015

Keywords

• nonn
• hard
• more

Examples

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

Crossrefs

Cf. A007749, A080778, A117141, A091415.

Programs

Magma

[n: n in [0..3*10^2] | IsPrime(Factorial(n)*2^n+1)]; // Vincenzo Librandi, Apr 05 2015

Mathematica

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

PARI

for(n=0,300,if(ispseudoprime(n!*2^n+1),print1(n,", "))) \\ Derek Orr, Apr 05 2015

Python

from sympy import factorial, isprime
for n in range(0,300):
    if isprime(factorial(n)*(2**n)+1):
        print(n, end=', ') # Stefano Spezia, Dec 06 2018

Formula

a(n) = A080778(n+1)/2 for n >= 2. - Amiram Eldar, Dec 06 2018

Extensions

a(6)-a(8), from the data at A080778, added by Amiram Eldar, Dec 06 2018