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Numbers k such that k![4] - 16 is prime, where k![4] = A007662(k) = quadruple factorial.
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%I #8 Apr 03 2023 10:36:13

%S 7,9,13,15,17,29,31,35,39,105,109,147,173,239,287,293,505,711,837,947,

%T 1015,1025,1977,2917,4035,4935,5935,7693,10911,11367,12029,14155,

%U 15221,17921,17961,20521,23053,32821,45147,45351,68057,78315

%N Numbers k such that k![4] - 16 is prime, where k![4] = A007662(k) = quadruple factorial.

%C a(43) > 10^5.

%C The first 5 primes associated with this sequence are: 5, 29, 569, 3449, 9929.

%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The top ten prime numbers: from the unpublished collections of R. Ondrejka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] - 16; x > 0 && PrimeQ[x]) &]

%Y Cf. A007662, A283553.

%K nonn

%O 1,1

%A _Robert Price_, Nov 06 2019