A289689 Numbers k such that k!6 - 16 is prime, where k!6 is the sextuple factorial number (A085158).

9, 15, 17, 65, 129, 135, 209, 225, 327, 357, 423, 1061, 1143, 3629, 4937, 6713, 33123, 79185, 88323, 89933

Offset: 1

Author

Robert Price, Jul 09 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 11, 389, 919, 8549258359016359, 17694587964658118355578965371540271859, ...

a(21) > 10^5.

Terms > 17 correspond to probable primes.

Examples

			17!6 - 16 = 17*11*5 - 16 = 919 is prime, so 17 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!6-16.
• 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[6, 50000], PrimeQ[MultiFactorial[#, 6] - 16] &]

Extensions

a(18)-a(20) from Robert Price, Aug 03 2018