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A288444 Numbers k such that k!6 + 16 is prime, where k!6 is the sextuple factorial number (A085158 ).

%I A288444 #7 Jul 05 2023 18:54:23
%S A288444 1,3,7,9,11,13,15,21,23,35,37,39,47,49,59,111,117,163,287,311,601,635,
%T A288444 855,895,2455,2929,3369,7147,10367,12311,13093,13611,14431,17305,27331
%N A288444 Numbers k such that k!6 + 16 is prime, where k!6 is the sextuple factorial number (A085158 ).
%C A288444 Corresponding primes are: 17, 19, 23, 43, 71, 107, 421, 8521, 21521, 21827591, 49579091, 295540261, 42061737041, 104463111041, ...
%C A288444 a(36) > 50000.
%C A288444 Terms > 49 correspond to probable primes.
%H A288444 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+16&amp;action=Search">PRP Records. Search for n!6+16.</a>
%H A288444 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 A288444 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A288444 11!6 + 16 = 11*5 + 16 = 71 is prime, so 11 is in the sequence.
%t A288444 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A288444 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 16] &]
%t A288444 Select[Range[1000],PrimeQ[Times@@Range[#,1,-6]+16]&] (* The program generates the first 24 terms of the sequence. To generate more, increase the Range constant. *)
%Y A288444 Cf. A007661, A037082, A084438, A123910, A242994.
%K A288444 nonn,more
%O A288444 1,2
%A A288444 _Robert Price_, Jun 09 2017