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A288885 Primes of the form k!3 + 3^9, where k!3 is the triple factorial number (A007661).

%I A288885 #11 Apr 14 2025 09:03:19
%S A288885 19687,19763,19963,20563,32003,229123,4208483,24364003,72642189283,
%T A288885 2324549446883,5577337931669523683,38900816605808456499219683,
%U A288885 26070192823309041523916819683
%N A288885 Primes of the form k!3 + 3^9, where k!3 is the triple factorial number (A007661).
%H A288885 Robert Price, <a href="/A288885/b288885.txt">Table of n, a(n) for n = 1..18</a>
%H A288885 Henri and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n3+3^9&amp;action=Search">PRP Records.Search for n!3+3^9</a>.
%H A288885 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 A288885 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>.
%F A288885 a(n) = 19683 + A007661(A265378(n)). - _Elmo R. Oliveira_, Apr 14 2025
%t A288885 MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
%t A288885 Select[Table[MultiFactorial[i, 3] + 3^9, {i, 0, 100}], PrimeQ[#]&]
%t A288885 Select[Table[Times@@Range[n,1,-3]+19683,{n,100}],PrimeQ] (* _Harvey P. Dale_, Sep 18 2023 *)
%Y A288885 Cf. A007661, A265378.
%K A288885 nonn
%O A288885 1,1
%A A288885 _Robert Price_, Jun 18 2017