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

0, 2, 4, 8, 72

Offset

1,2

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

Links

Table of n, a(n) for n=1..5.

Example

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

Mathematica

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

Prog

(PARI) for(n=1, 1e3, if(isprime(k=(n!+2^n+1)), print1(n", ")))
(Magma) [n: n in [1..300] | IsPrime(Factorial(n)+2^n+1)]; // Vincenzo Librandi, Aug 30 2015
(PFGW) ABC2 $a! + 2^$a + 1
a: from 0 to 30000
Charles R Greathouse IV, Sep 08 2015

Crossrefs

Cf. A007611.

Sequence in context: A270372 A018507 A018523 * A204548 A018532 A270381

Adjacent sequences: A261711 A261712 A261713 * A261715 A261716 A261717

Keyword

nonn,more,hard

Author

Altug Alkan, Aug 29 2015

Status

approved