A289698 Numbers k such that k!6 - 27 is prime, where k!6 is the sextuple factorial number (A085158).

10, 14, 16, 34, 46, 86, 116, 130, 344, 410, 446, 746, 824, 1580, 1682, 1918, 2684, 2710, 4172, 4754, 6976, 7418, 8788, 11756, 13546, 16048, 17192, 19624, 24026, 28510, 32758, 41780, 42740, 45856, 51050

Offset: 1

Author

Robert Price, Jul 09 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 13, 197, 613, 13404133, 24663654373, 37455569511954513919973, ...

a(36) > 10^5.

Terms > 46 correspond to probable primes.

Examples

			14!6 - 27 = 14*8*2 - 27 = 197 is prime, so 14 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!6-27.
• 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[10, 50000], PrimeQ[MultiFactorial[#, 6] - 27] &]

Extensions

a(35) from Robert Price, Aug 04 2018