A247463 Numbers n such that n!3 - 3^3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

8, 11, 13, 22, 29, 49, 56, 61, 103, 142, 149, 257, 319, 365, 680, 736, 737, 749, 947, 974, 1040, 4277, 4678, 9961, 10652, 15545, 18064, 31325, 34918, 41032

Offset: 1

Author

Robert Price, Sep 17 2014

Keywords

• nonn
• more

Comments

Large terms correspond to probable primes.

a(31) > 50000.

Examples

			11!3-27 = 11*8*5*2-27 = 853 is prime, so 11 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!3-27
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester
• Eric Weisstein's World of Mathematics, Multifactorial

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 27], AppendTo[lst, n]], {n, 100}];lst
Select[Range[6,1100],PrimeQ[Times@@Range[#,1,-3]-27]&] (* Harvey P. Dale, Mar 16 2023 *)