A261714 Numbers n such that n! + 2^n + 1 is prime.

0, 2, 4, 8, 72

Offset: 1

Author

Altug Alkan, Aug 29 2015

Keywords

• nonn
• more
• hard

Comments

Inspired by A007611.

First three prime numbers of the form n! + 2^n +1 with positive n value are 7, 41, 40577.

a(5) > 30000. - Giovanni Resta, Aug 30 2015

Examples

			For n=2, n! + 2^n + 1 = 2! + 2^2 + 1 = 7, which is prime.
		

Crossrefs

Cf. A007611.

Programs

Magma

[n: n in [1..300] | IsPrime(Factorial(n)+2^n+1)]; // Vincenzo Librandi, Aug 30 2015

Mathematica

Select[Range@ 2000, PrimeQ[#! + 2^# + 1] &] (* Michael De Vlieger, Aug 29 2015 *)

PARI

for(n=1, 1e3, if(isprime(k=(n!+2^n+1)), print1(n", ")))

PFGW

ABC2 $a! + 2^$a + 1
a: from 0 to 30000
Charles R Greathouse IV, Sep 08 2015