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A291348 Numbers k such that k!4 + 2^7 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

%I A291348 #9 Feb 26 2023 13:08:49
%S A291348 3,7,9,11,15,19,29,37,91,123,151,197,415,763,1817,2981,3977,4199,
%T A291348 11667,12865,16873,19449,27213,31581,64877,65401
%N A291348 Numbers k such that k!4 + 2^7 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C A291348 Corresponding primes are: 131, 149, 173, 359, 3593, 65963, 151412753, ...
%C A291348 a(27) > 10^5.
%C A291348 Terms > 37 correspond to probable primes.
%H A291348 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+128.</a>
%H A291348 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 A291348 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A291348 15!4 + 2^7 = 15*11*7*3*1 + 128 = 3593 is prime, so 15 is in the sequence.
%t A291348 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A291348 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^7] &]
%t A291348 Select[Range[3000],PrimeQ[Times@@Range[#,1,-4]+128]&] (* _Harvey P. Dale_, Feb 26 2023 *)
%Y A291348 Cf. A007662, A037082, A084438, A123910, A242994.
%K A291348 nonn,more
%O A291348 1,1
%A A291348 _Robert Price_, Aug 22 2017
%E A291348 a(25)-a(26) from _Robert Price_, Sep 25 2019