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A329177 Numbers k such that k![4] - 256 is prime, where k![4] = A007662(k) = quadruple factorial.

%I A329177 #10 Apr 03 2023 10:36:13
%S A329177 15,17,19,21,23,25,33,39,41,43,53,63,67,73,157,167,181,195,221,327,
%T A329177 363,419,849,861,1233,1265,1599,2413,2515,4009,8291,8475,10685,13957,
%U A329177 17453,18409,19117,22739,33313,37861,59703,64983,80697
%N A329177 Numbers k such that k![4] - 256 is prime, where k![4] = A007662(k) = quadruple factorial.
%C A329177 a(44) > 10^5.
%C A329177 The first 5 primes associated with this sequence are: 3209, 9689, 65579, 208589, 1513949.
%H A329177 C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/MultifactorialPrime.html">multifactorial prime</a>
%H A329177 C. Caldwell and H. Dubner (Eds): <a href="https://t5k.org/lists/top_ten/">The top ten prime numbers: from the unpublished collections of R. Ondrejka</a> (May 2001), Table 21 F, p. 75.
%H A329177 Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.
%H A329177 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>
%t A329177 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A329177 Select[Range[1000], (x = MultiFactorial[#, 4] - 256; x > 0 && PrimeQ[x]) &]
%t A329177 Select[Range[10,1600],PrimeQ[Times@@Range[#,1,-4]-256]&] (* The program generates the first 27 terms of the sequence. To generate more, increase the second Range constant but the program may take a long time to run. *) (* _Harvey P. Dale_, Aug 01 2022 *)
%Y A329177 Cf. A007662, A283553.
%K A329177 nonn
%O A329177 1,1
%A A329177 _Robert Price_, Nov 07 2019