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Numbers k such that k!6 + 8 is prime, where k!6 is the sextuple factorial number (A085158 ).
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%I #6 Jun 05 2017 23:09:15

%S 3,5,21,29,41,65,243,305,389,509,819,1653,7493,8613,8619,10257,11829,

%T 12977,15651,24341,29367,31629,40173

%N Numbers k such that k!6 + 8 is prime, where k!6 is the sextuple factorial number (A085158 ).

%C Corresponding primes are: 11, 13, 8513, 623653, 894930583, 8549258359016383, ...

%C a(24) > 50000.

%C Terms > 41 correspond to probable primes.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+8&amp;action=Search">PRP Records. Search for n!6+8.</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 21!6 + 8 = 21*15*9*3 + 8 = 8513 is prime, so 21 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] + 8] &]

%Y Cf. A007661, A037082, A084438, A123910, A242994.

%K nonn,more

%O 1,1

%A _Robert Price_, Jun 05 2017