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%I #15 Nov 29 2018 17:52:05
%S 17,19,23,31,37,47,65,151,157,251,283,371,391,635,779,799,1517,1799,
%T 3355,24619,40375,40793,53135,79427
%N Numbers k such that k!6 - 6 is prime, where k!6 is the sextuple factorial number (A085158).
%C Corresponding primes are: 929, 1723, 21499, 1339969, 49579069, 42061737019, ...
%C a(25) > 10^5.
%C Terms > 65 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6-6&action=Search">PRP Records. Search for n!6-6.</a>
%H 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 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e 17!6 - 6 = 17*11*5 - 6 = 929 is prime, so 17 is in the sequence.
%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t Select[Range[6, 50000], PrimeQ[MultiFactorial[#, 6] - 6] &]
%Y Cf. A007661, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Jul 09 2017
%E a(23)-a(24) from _Robert Price_, Aug 03 2018
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