

A261714


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


2




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



