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A291122 Numbers k such that k!4 + 2^2 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

%I A291122 #13 Sep 16 2024 19:55:58
%S A291122 0,1,3,15,17,19,23,25,27,29,35,49,63,79,87,105,139,319,339,409,441,
%T A291122 477,1023,1107,1517,1557,1625,4215,5297,6291,6499,7357,11639,12963,
%U A291122 13989,15825,19993,20535,35391,58483,69247
%N A291122 Numbers k such that k!4 + 2^2 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C A291122 Corresponding primes are: 5, 5, 7, 3469, 9949, 65839, 1514209, 5221129, 40883539, ...
%C A291122 a(42) > 10^5.
%C A291122 Terms > 35 correspond to probable primes.
%H A291122 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+4.</a>
%H A291122 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 A291122 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A291122 15!4 + 2^2 = 15*11*7*3*1 + 4 = 3469 is prime, so 15 is in the sequence.
%t A291122 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A291122 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^2] &]
%t A291122 Select[Range[0,4300],PrimeQ[Times@@Range[#,1,-4]+4]&] (* The program generates the first 28 terms of the sequence. *) (* _Harvey P. Dale_, Sep 16 2024 *)
%Y A291122 Cf. A007662, A037082, A084438, A123910, A242994.
%K A291122 nonn,more
%O A291122 1,3
%A A291122 _Robert Price_, Aug 17 2017
%E A291122 a(40)-a(41) from _Robert Price_, Sep 25 2019