A263482 Numbers k such that k! + 2^k + 11 or k! + 2^k - 11 is prime.

0, 2, 3, 4, 5, 6, 7, 9, 15, 34, 41, 79, 99, 379, 2183

Offset: 1

Author

Altug Alkan, Oct 19 2015

Keywords

• nonn
• more

Comments

Is there some k such that k! + 2^k + 11 and k! + 2^k - 11 are prime?

a(16) > 20000. - Michael S. Branicky, Jul 25 2024

Examples

			For k = 0, k! + 2^k + 11 = 0! + 2^0 + 11 = 13, which is prime.
For k = 3, k! + 2^k - 11 = 3! + 2^3 - 11 = 3, which is prime.
		

Crossrefs

Cf. A007611, A261714, A263469.

Programs

Mathematica

Select[Range[0, 400], Or[PrimeQ[#! + 2^# + 11], PrimeQ[#! + 2^# - 11]] &] (* Michael De Vlieger, Nov 17 2015 *)
Select[Range[0,500],AnyTrue[#!+2^#+{11,-11},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2019 *)

PARI

for(n=0, 1e3, if(isprime(n!+2^n-11) || isprime(n!+2^n+11), print1(n", ")))

PARI

is(n)=my(N=n!+2^n); ispseudoprime(N-11) || ispseudoprime(N+11) \\ Charles R Greathouse IV, Nov 17 2015

Extensions

a(14) from Charles R Greathouse IV, Nov 17 2015

a(15) from Michael S. Branicky, Jun 17 2023