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Numbers k such that k![4] - 512 is prime, where k![4] = A007662(k) = quadruple factorial.
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%I #6 Apr 03 2023 10:36:13

%S 13,15,17,19,21,23,25,35,39,47,67,71,89,93,113,153,163,185,201,267,

%T 427,491,871,1645,3075,3351,3435,5385,7893,10649,15597,44641,50039,

%U 57269,67647,83061,89717

%N Numbers k such that k![4] - 512 is prime, where k![4] = A007662(k) = quadruple factorial.

%C a(38) > 10^5.

%C The first 5 primes associated with this sequence are: 73, 2953, 9433, 65323, 208333.

%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The top ten prime numbers: from the unpublished collections of R. Ondrejka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] - 512; x > 0 && PrimeQ[x]) &]

%Y Cf. A007662, A283553.

%K nonn

%O 1,1

%A _Robert Price_, Nov 07 2019