A265201 -id:A265201 - cp's OEIS frontend

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

Robert Price, Jan 09 2016

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

a(31) > 50000.

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

Henri & Renaud Lifchitz, PRP Records. Search for n!3-19683.
Joe McLean, Interesting Sources of Probable Primes

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

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 *)

A289825 Primes of the form k!3 - 59049, where k!3 is the triple factorial number (A007661).

Original entry on oeis.org

1047511, 4129751, 24285271, 2504843351, 126757680265156951, 7368624314106569113540951, 38900816605808456499140951, 663800167477016615356604425212847831700575205814331164458540403251687739883519999999940951

Offset: 1

Robert Price, Jul 12 2017

nonn

Robert Price, Table of n, a(n) for n = 1..9
Henri & Renaud Lifchitz, PRP Records.Search for n!3-59049.
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A007661, A265201.

MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 3] - 59049, {i, 17, 100}], PrimeQ[#]&]

a(n) = A007661(A265201(n)) - 59049. - Elmo R. Oliveira, Feb 25 2025

cp's OEIS Frontend

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

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