A267029 Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

16, 17, 34, 38, 49, 62, 74, 97, 125, 137, 146, 178, 188, 235, 664, 863, 916, 1988, 2059, 2837, 5353, 5489, 7483, 9344, 12631, 13796, 17122, 23134, 30409, 33077

Offset

1,1

Comments

Corresponding primes are 38557, 189757, 17961239276317, 3091650738156317, ... .

a(31) > 50000.

Links

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

Henri & Renaud Lifchitz, PRP Records. Search for n!3-19683.

Joe McLean, Interesting Sources of Probable Primes

Example

16!3 - 3^9 = 16*13*10*7*4*1 - 19683 = 58240 - 19683 = 38557 is prime, so 16 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[15, 50000], PrimeQ[MultiFactorial[#, 3] - 3^9] &]
Select[Range[12, 33100], PrimeQ[Times@@Range[#, 1, -3]-19683]&] (* Harvey P. Dale, Jan 25 2021 *)

Crossrefs

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145, A265201.

Sequence in context: A041516 A041514 A041512 * A070869 A101196 A064637

Adjacent sequences: A267026 A267027 A267028 * A267030 A267031 A267032

Keyword

hard,more,nonn

Author

Robert Price, Jan 09 2016

Status

approved