A288447 Numbers k such that k!6 + 27 is prime, where k!6 is the sextuple factorial number (A085158 ).

2, 4, 8, 10, 14, 20, 22, 26, 32, 40, 110, 116, 142, 148, 200, 370, 854, 1166, 1594, 2164, 4424, 5942, 9086, 13300, 15224, 20482, 22940, 27478, 47486

Offset: 1

Author

Robert Price, Jun 09 2017

Keywords

• nonn
• more

Comments

Corresponding primes are: 29, 31, 43, 67, 251, 4507, 14107, 116507, 3727387, 536166427, ...

a(30) > 50000.

Terms > 40 correspond to probable primes.

Examples

			10!6 + 27 = 10*4 + 27 = 67 is prime, so 10 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[0, 50000], PrimeQ[MultiFactorial[#, 6] + 27] &]
Select[Range[48000],PrimeQ[Times@@Range[#,1,-6]+27]&] (* Harvey P. Dale, Aug 10 2021 *)