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A291350 Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

%I A291350 #7 Sep 25 2019 15:03:02
%S A291350 9,11,13,17,19,21,29,31,33,35,67,103,111,129,179,355,713,799,921,1013,
%T A291350 1389,1543,2097,2287,3657,4115,7031,10689,11715,16401,16893,19497,
%U A291350 29737,35615
%N A291350 Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C A291350 Corresponding primes are: 557, 743, 1097, 10457, 66347, 209357, 151413137, ...
%C A291350 a(35) > 10^5.
%C A291350 Terms > 35 correspond to probable primes.
%H A291350 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n%214%2B4&amp;action=Search">PRP Records. Search for n!4+512.</a>
%H A291350 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 A291350 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A291350 11!4 + 2^9 = 11*7*3*1 + 512 = 743 is prime, so 11 is in the sequence.
%t A291350 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A291350 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^9] &]
%Y A291350 Cf. A007662, A037082, A084438, A123910, A242994.
%K A291350 nonn,more
%O A291350 1,1
%A A291350 _Robert Price_, Aug 22 2017