A267382 - OEIS

A267382

Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

13, 14, 16, 19, 22, 23, 26, 38, 64, 104, 137, 203, 296, 346, 347, 379, 481, 568, 899, 1162, 1603, 2614, 5698, 5846, 9253, 9565, 9848, 10406, 16051, 18377, 23110, 26026, 26120, 28994

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OFFSET

1,1

COMMENTS

Corresponding primes are: 1453, 10133, 56053, 1104373, 24342133, 2504900213, 3091650738173813, ... .

a(35) > 50000.

Terms > 26 correspond to probable primes.

LINKS

Table of n, a(n) for n=1..34.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-2187.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

EXAMPLE

13!3 - 3^7 = 13*10*7*4 - 2187 = 1453 is prime, so 13 is in the sequence.

MATHEMATICA

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];

Select[Range[13, 50000], PrimeQ[MultiFactorial[#, 3] - 3^7] &]

Select[Range[12, 6000], PrimeQ[Times@@Range[#, 1, -3]-2187]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Aug 14 2024 *)

CROSSREFS

Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.

Sequence in context: A272022 A079495 A076204 * A135024 A173036 A241749

Adjacent sequences: A267379 A267380 A267381 * A267383 A267384 A267385

KEYWORD

nonn,more

AUTHOR

Robert Price, Jan 13 2016

STATUS

approved