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

1,1

Comments

Large terms correspond to probable primes.

a(31) > 50000.

Links

Table of n, a(n) for n=1..30.

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

Example

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

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 *)

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Sequence in context: A363374 A337491 A106670 * A308562 A254671 A265412

Adjacent sequences: A247460 A247461 A247462 * A247464 A247465 A247466

Keyword

nonn,more

Author

Robert Price, Sep 17 2014

Status

approved