A243078 Numbers k such that k!3 - 3^2 is prime, where k!3 = k!!! is a triple factorial number (A007661).

7, 8, 10, 13, 16, 17, 20, 23, 28, 29, 32, 43, 46, 47, 53, 56, 59, 61, 76, 95, 107, 139, 148, 218, 349, 764, 1009, 1130, 1183, 1429, 1516, 2072, 2471, 4937, 10204, 13993, 16249, 18166, 25733, 29033, 40090

Offset

1,1

Comments

a(42) > 50000.

k=2 and k=4 produce values (-7 and -5) whose absolute value is a prime.

Terms > 2000 correspond to probable primes.

Links

Table of n, a(n) for n=1..41.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-9.

OpenPFGW Project, Primality Tester

Example

17!3 - 3^2 = 17*14*11*8*5*2 - 9 = 209431 is prime, so 17 is in the sequence. - Jens Kruse Andersen, Aug 20 2014

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]-3^2], AppendTo[lst, n]], {n, 50000}]; lst

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994.

Sequence in context: A175222 A067529 A080113 * A048588 A141676 A127164

Adjacent sequences: A243075 A243076 A243077 * A243079 A243080 A243081

Keyword

nonn,more

Author

Robert Price, May 30 2014

Extensions

a(41) from Robert Price, Sep 19 2014

Status

approved