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A267382 Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).

%I A267382 #15 Aug 14 2024 14:34:02
%S A267382 13,14,16,19,22,23,26,38,64,104,137,203,296,346,347,379,481,568,899,
%T A267382 1162,1603,2614,5698,5846,9253,9565,9848,10406,16051,18377,23110,
%U A267382 26026,26120,28994
%N A267382 Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C A267382 Corresponding primes are: 1453, 10133, 56053, 1104373, 24342133, 2504900213, 3091650738173813, ... .
%C A267382 a(35) > 50000.
%C A267382 Terms > 26 correspond to probable primes.
%H A267382 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-2187&amp;action=Search">PRP Records. Search for n!3-2187.</a>
%H A267382 Joe McLean, <a href="http://web.archive.org/web/20091027034731/http://uk.geocities.com/nassarawa%40btinternet.com/probprim2.htm">Interesting Sources of Probable Primes</a>
%H A267382 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A267382 13!3 - 3^7 = 13*10*7*4 - 2187 = 1453 is prime, so 13 is in the sequence.
%t A267382 MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
%t A267382 Select[Range[13, 50000], PrimeQ[MultiFactorial[#, 3] - 3^7] &]
%t A267382 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 *)
%Y A267382 Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.
%K A267382 nonn,more
%O A267382 1,1
%A A267382 _Robert Price_, Jan 13 2016