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%I #11 Jul 09 2020 15:32:47
%S 0,1,5,7,11,13,17,19,23,25,41,67,71,101,109,151,163,181,233,241,265,
%T 355,433,563,767,997,1465,1681,1861,1913,2411,2539,2777,13433,22355,
%U 30895,44605
%N Numbers k such that k!6 + 12 is prime, where k!6 is the sextuple factorial number (A085158 ).
%C Corresponding primes are: 13, 13, 17, 19, 67, 103, 947, 1741, 21517, 43237, 894930587, ...
%C a(37) > 50000.
%C Terms > 41 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+12&action=Search">PRP Records. Search for n!6+12.</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 11!6 + 12 = 11*5 + 12 = 67 is prime, so 11 is in the sequence.
%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 12] &]
%t Select[Range[0, 45000], PrimeQ[Times @@ Range[#, 1, -6] + 12] &] (* _Harvey P. Dale_, Jul 09 2020 *)
%Y Cf. A007661, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,3
%A _Robert Price_, Jun 05 2017
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