A099351 Numbers k such that 5*k! - 1 is prime.

3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521, 1279, 1750, 2204, 2473, 4193, 5181, 10080

Offset: 1

Author

Brian Kell, Oct 12 2004

Keywords

• nonn
• more

Comments

a(15) > 1879. - Jinyuan Wang, Feb 04 2020

a(17) > 3500. - Michael S. Branicky, Mar 06 2021

Examples

			k = 5 is here because 5*5! - 1 = 599 is prime.
		

Links

• Index entries for sequences related to numbers of primes of the form k*n!+-1

Crossrefs

Cf. A002982, A076133, A076134, A099350, A180627, A180628, A180629, A180630, A180631.

Programs

Maple

for n from 0 to 1000 do if isprime(5*n! - 1) then print(n) end if end do;

Mathematica

Select[Range[550],PrimeQ[5#!-1]&] (* Harvey P. Dale, Nov 27 2013 *)

PARI

is(n)=ispseudoprime(5*n!-1) \\ Charles R Greathouse IV, Jun 13 2017

Python

from sympy import isprime
from math import factorial
print([k for k in range(300) if isprime(5*factorial(k) - 1)]) # Michael S. Branicky, Mar 05 2021

Extensions

a(13)-a(14) from Jinyuan Wang, Feb 04 2020

a(15)-a(16) from Michael S. Branicky, Mar 05 2021

a(17)-a(18) from Michael S. Branicky, Apr 03 2023

a(19) from Michael S. Branicky, Jul 12 2024