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A261344 Numbers n such that n!3 - 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

%I A261344 #28 Apr 27 2022 19:16:15
%S A261344 16,17,20,25,26,35,37,47,88,94,125,127,134,326,328,368,398,425,698,
%T A261344 700,734,1303,1427,2011,2542,2699,3938,4214,5137,6314,8669,9041,12494,
%U A261344 13520,14609,23732,41399,43867,49471
%N A261344 Numbers n such that n!3 - 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C A261344 n=5 and n=8 produce values (-6551 and -6481) whose absolute value is a prime.
%C A261344 Corresponding primes are: 51679, 202879, 4182239, 608601439, 2504895839, ...
%C A261344 a(40) > 50000.
%C A261344 Terms > 26 correspond to probable primes.
%H A261344 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-6561&amp;action=Search">PRP Records. Search for n!3-6561.</a>
%H A261344 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 A261344 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A261344 16!3 - 3^8 = 16*13*10*7*4*1 - 6561 = 51679 is prime, so 16 is in the sequence.
%t A261344 MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
%t A261344 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] - 3^8] &]
%t A261344 Select[Range[14,800],PrimeQ[Times@@Range[#,1,-3]-6561]&] (* The program generates the first 21 terms of the sequence. To generate more, increase the Range constant. *) (* _Harvey P. Dale_, Apr 27 2022 *)
%o A261344 (PARI) for(n=1, 1e3, if(ispseudoprime(prod(i=0, floor((n-1)/3), n-3*i) - 3^8), print1(n, ", "))) \\ _Altug Alkan_, Nov 18 2015
%Y A261344 Cf. A007661, A037082, A084438, A123910, A242994.
%K A261344 nonn,more
%O A261344 1,1
%A A261344 _Robert Price_, Nov 18 2015