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%I #19 May 22 2021 16:08:39
%S 3,4,6,8,20,26,36,50,60,114,135,138,248,315,351,429,642,5505,8793,
%T 12086,13580,23109,34626,34706,56282,57675,58298
%N Positive integers n such that n!!! - 1 = A007661(n) - 1 is prime.
%C The search for multifactorial primes started by Ray Ballinger is now continued by a team of volunteers on the website of Ken Davis (see link).
%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes.</a>
%H Ken Davis, <a href="http://mfprimes.free-dc.org/mfdata/f03m.html">Results for n!3-1.</a>
%H ProthSearch.net (on web.archive.org), <a href="http://web.archive.org/web/20050220234200/http://www.prothsearch.net/n3minus.txt">n3minus.txt</a>
%e a(4)=8 since 8!!!-1 = 8*5*2-1 = 79 is the 4th prime of that form.
%e 26!!!-1 = 2504902399 is prime.
%t multiFactorial[n_, k_] := If[n < 1, 1, n * multiFactorial[n - k, k]];
%t Select[Range[0, 1000], PrimeQ[multiFactorial[#, 3] - 1] & ] (* _Robert Price_, Apr 19 2019 *)
%t Select[Range[650], PrimeQ[Times @@ Range[#, 1, -3] - 1] &] (* The program generates the first 17 terms of the sequence. To generate more, change the Range constant but the program may take a long time to run. *) (* _Harvey P. Dale_, May 22 2021 *)
%o (PARI) A007661(n) = prod(i=1,(n-1)\3,n-=3,n+!n) /* newline */ for(n=1,999,if(isprime(A007661(n)-1),print1(n","))) - _M. F. Hasler_, Nov 26 2007
%Y Cf. A007661, A135726, A037082, A037083.
%K hard,nonn
%O 1,1
%A _Hugo Pfoertner_, Jun 25 2003
%E Missing 26 inserted by _M. F. Hasler_, Nov 26 2007
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
%E Edited by _N. J. A. Sloane_, Feb 11 2009 at the suggestion of M. F. Hasler
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