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

0, 2, 3, 4, 5, 6, 7, 15, 17, 21, 42, 57, 99, 312, 372, 15030

Offset: 1

Author

Altug Alkan, Oct 19 2015

Keywords

• nonn
• more

Comments

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

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

Examples

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

Crossrefs

Cf. A007611, A261714, A263482.

Programs

Mathematica

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

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

Extensions

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

a(16) from Michael S. Branicky, Jul 25 2024