A289696 Numbers k such that k!6 - 18 is prime, where k!6 is the sextuple factorial number (A085158).

11, 13, 23, 25, 35, 85, 89, 91, 103, 127, 161, 265, 295, 385, 605, 719, 913, 1379, 1423, 1481, 1603, 2129, 2603, 3893, 4739, 6461, 7249, 7549, 8149, 10633, 14447, 27463, 30323, 33991, 35821, 42221, 46525, 59057

Offset: 1

Author

Robert Price, Jul 09 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 37, 73, 21487, 43207, 21827557, 11510631741140058401857, ...

a(39) > 10^5.

Terms > 35 correspond to probable primes.

Examples

			13!6 - 18 = 13*7 - 18 = 73 is prime, so 13 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!6-18.
• 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[9, 50000], PrimeQ[MultiFactorial[#, 6] - 18] &]
Select[Range[11,60000],PrimeQ[Times@@Range[#,1,-6]-18]&] (* Harvey P. Dale, Aug 10 2019 *)

Extensions

a(38) from Robert Price, Aug 03 2018