A288155 Numbers k such that k!6 + 12 is prime, where k!6 is the sextuple factorial number (A085158 ).

0, 1, 5, 7, 11, 13, 17, 19, 23, 25, 41, 67, 71, 101, 109, 151, 163, 181, 233, 241, 265, 355, 433, 563, 767, 997, 1465, 1681, 1861, 1913, 2411, 2539, 2777, 13433, 22355, 30895, 44605

Offset: 1

Author

Robert Price, Jun 05 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 13, 13, 17, 19, 67, 103, 947, 1741, 21517, 43237, 894930587, ...

a(37) > 50000.

Terms > 41 correspond to probable primes.

Examples

			11!6 + 12 = 11*5 + 12 = 67 is prime, so 11 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!6+12.
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 12] &]
Select[Range[0, 45000], PrimeQ[Times @@ Range[#, 1, -6] + 12] &] (* Harvey P. Dale, Jul 09 2020 *)