A263469 Numbers n such that n! + 2^n + 3 or n! + 2^n - 3 is prime.

0, 2, 3, 4, 5, 6, 7, 15, 17, 21, 42, 57, 99, 312, 372

Offset

1,2

Comments

Both n! + 2^n + 3 and n! + 2^n - 3 are prime for n = 3 or 4. Are there any others?

No more terms below 10^4. - Charles R Greathouse IV, Nov 17 2015

Links

Table of n, a(n) for n=1..15.

Example

For n=0, n! + 2^n + 3 = 0! + 2^0 + 3 = 5, which is prime.
For n=2, n! + 2^n - 3 = 2! + 2^2 - 3 = 3, which is prime.

Mathematica

Select[Range[0, 10^3], Or[PrimeQ[#! + 2^# + 3], PrimeQ[#! + 2^# - 3]] &] (* Michael De Vlieger, Oct 20 2015 *)

Prog

(PARI) for(n=0, 1e3, if(isprime(n!+2^n-3) || isprime(n!+2^n+3), print1(n", ")))
(PARI) is(n)=my(N=n!+2^n); ispseudoprime(N-3) || ispseudoprime(N+3) \\ Charles R Greathouse IV, Nov 17 2015

Crossrefs

Cf. A007611, A261714, A263482.

Sequence in context: A115308 A171649 A146028 * A165804 A055402 A274839

Adjacent sequences: A263466 A263467 A263468 * A263470 A263471 A263472

Keyword

nonn,more

Author

Altug Alkan, Oct 19 2015

Extensions

a(14)-a(15) from Michael De Vlieger, Oct 20 2015

Status

approved