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

1,3

Comments

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

a(37) > 50000.

Terms > 41 correspond to probable primes.

Links

Table of n, a(n) for n=1..37.

Henri & Renaud Lifchitz, PRP Records. Search for n!6+12.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

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

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 *)

Crossrefs

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

Sequence in context: A363999 A290729 A314295 * A135775 A353686 A219016

Adjacent sequences: A288152 A288153 A288154 * A288156 A288157 A288158

Keyword

nonn,more

Author

Robert Price, Jun 05 2017

Status

approved