A249400 Numbers n such that n!3 + 3 is prime, where n!3 = n!!! is a triple factorial number (A007661).

2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 19, 20, 26, 28, 29, 32, 41, 56, 61, 77, 100, 169, 181, 205, 338, 347, 955, 1952, 2197, 2428, 2960, 3430, 4618, 7478, 8209, 8422, 9235, 11107, 13481, 18194, 19229, 29854, 46532

Offset: 1

Author

Robert Price, Oct 27 2014

Keywords

• nonn
• more

Comments

Large terms correspond to probable primes.

a(44) > 50000.

Examples

			11!3+3 = 11*8*5*2+3 = 883 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] + 3], AppendTo[lst, n]], {n, 100}];lst