A289697 Numbers k such that k!6 - 24 is prime, where k!6 is the sextuple factorial number (A085158).

9, 11, 13, 17, 23, 25, 29, 31, 37, 43, 53, 65, 71, 77, 79, 115, 119, 151, 173, 559, 793, 1571, 1715, 1807, 1861, 2047, 2215, 3491, 4751, 6631, 9089, 9139, 9253, 25811, 29491, 29495, 54335, 54991, 66535, 72365

Offset: 1

Author

Robert Price, Jul 09 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 3, 31, 67, 911, 21481, 43201, 623621, 1339951, ...

a(41) > 10^5.

Terms > 43 correspond to probable primes.

Examples

			13!6 - 4 = 13*7*1 - 24 = 67 is prime, so 13 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!6-24.
• 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] - 24] &]
Select[Range[8,5000],PrimeQ[Times@@Range[#,1,-6]-24]&] (* Harvey P. Dale, Dec 01 2018 *)

Extensions

a(37)-a(40) from Robert Price, Aug 03 2018