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A264867 Numbers n such that n!3 + 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

%I A264867 #16 Mar 08 2023 16:07:15
%S A264867 2,5,10,26,34,35,37,59,68,76,104,106,188,193,242,278,287,290,572,772,
%T A264867 773,1304,2384,2716,3715,4562,6706,11489,11711,21602,24295,24775,
%U A264867 27224,29935,37856
%N A264867 Numbers n such that n!3 + 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C A264867 Corresponding primes are 6563, 6571, 6841, 2504908961, 17961239302561, 81359229958561, 664565853958561, ...
%C A264867 Terms > 68 correspond to probable primes.
%C A264867 a(36) > 50000.
%H A264867 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+6561&amp;action=Search">PRP Records. Search for n!3+3^8</a>
%H A264867 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 A264867 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A264867 10!3 + 3^4 = 10*7*4*1 + 6561 = 6841 is prime, so 10 is in the sequence.
%t A264867 MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
%t A264867 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^8] &]
%t A264867 Select[Range[800],PrimeQ[6561+Times@@Range[#,1,-3]]&] (* _Harvey P. Dale_, Mar 08 2023 *)
%o A264867 (PARI) is(n)=ispseudoprime(n!!! + 3^8) \\ _Anders Hellström_, Nov 27 2015
%o A264867 (PARI) tf(n) = prod(i=0,(n-1)\3, n-3*i);
%o A264867 for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^8), print1(n , ", "))) \\  _Altug Alkan_, Dec 03 2015
%Y A264867 Cf. A007661, A037082, A084438, A243078.
%K A264867 nonn,more
%O A264867 1,1
%A A264867 _Robert Price_, Nov 26 2015