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A289698 Numbers k such that k!6 - 27 is prime, where k!6 is the sextuple factorial number (A085158).

%I A289698 #14 Nov 29 2018 16:21:54
%S A289698 10,14,16,34,46,86,116,130,344,410,446,746,824,1580,1682,1918,2684,
%T A289698 2710,4172,4754,6976,7418,8788,11756,13546,16048,17192,19624,24026,
%U A289698 28510,32758,41780,42740,45856,51050
%N A289698 Numbers k such that k!6 - 27 is prime, where k!6 is the sextuple factorial number (A085158).
%C A289698 Corresponding primes are: 13, 197, 613, 13404133, 24663654373, 37455569511954513919973, ...
%C A289698 a(36) > 10^5.
%C A289698 Terms > 46 correspond to probable primes.
%H A289698 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6-27&amp;action=Search">PRP Records. Search for n!6-27.</a>
%H A289698 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 A289698 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A289698 14!6 - 27 = 14*8*2 - 27 = 197 is prime, so 14 is in the sequence.
%t A289698 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A289698 Select[Range[10, 50000], PrimeQ[MultiFactorial[#, 6] - 27] &]
%Y A289698 Cf. A007661, A037082, A084438, A123910, A242994.
%K A289698 nonn,more
%O A289698 1,1
%A A289698 _Robert Price_, Jul 09 2017
%E A289698 a(35) from _Robert Price_, Aug 04 2018