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%I #7 Dec 13 2015 08:08:10
%S 4,8,10,11,14,17,20,22,29,32,44,56,61,173,202,211,215,241,388,410,416,
%T 569,583,680,823,964,1271,1732,2309,2335,2404,2765,3019,3047,4670,
%U 5209,6320,6817,7531,9923,11243,14912,17969,21193,28940
%N Numbers n such that n!3 + 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C Corresponding primes are: 19687, 19763, 19963, 20563, 32003, 229123, 4208483, 24364003, 72642189283, ...
%C a(46) > 50000.
%C Terms > 61 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+19683&action=Search">PRP Records. Search for n!3+19683.</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>
%H OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e 11!3 + 3^9 = 11*8*5*2 + 19683 = 20563 is prime, so 11 is in the sequence.
%t MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^9] &]
%o (PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
%o for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^9), print1(n , ", "))) \\ _Altug Alkan_, Dec 07 2015
%Y Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.
%K nonn,more
%O 1,1
%A _Robert Price_, Dec 07 2015
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