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Numbers k such that k![4] - 256 is prime, where k![4] = A007662(k) = quadruple factorial.
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%I #10 Apr 03 2023 10:36:13

%S 15,17,19,21,23,25,33,39,41,43,53,63,67,73,157,167,181,195,221,327,

%T 363,419,849,861,1233,1265,1599,2413,2515,4009,8291,8475,10685,13957,

%U 17453,18409,19117,22739,33313,37861,59703,64983,80697

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

%C a(44) > 10^5.

%C The first 5 primes associated with this sequence are: 3209, 9689, 65579, 208589, 1513949.

%H C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/MultifactorialPrime.html">multifactorial prime</a>

%H 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The top ten prime numbers: from the unpublished collections of R. Ondrejka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 Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.

%H 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 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];

%t Select[Range[1000], (x = MultiFactorial[#, 4] - 256; x > 0 && PrimeQ[x]) &]

%t 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 Cf. A007662, A283553.

%K nonn

%O 1,1

%A _Robert Price_, Nov 07 2019