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A265201 Numbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).

%I A265201 #8 Apr 07 2025 13:26:24
%S A265201 19,20,22,26,41,55,56,152,155,316,347,383,500,556,646,656,748,976,
%T A265201 1433,2213,2680,2911,3373,4799,4964,7189,8798,9871,14069,14627,16657,
%U A265201 20230,24137,24430,28331,36313,41522,43031,46072,47719
%N A265201 Numbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C A265201 Corresponding primes are 1047511, 4129751, 24285271, 2504843351, 126757680265156951, ... .
%C A265201 a(41) > 50000.
%H A265201 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-59049&amp;action=Search">PRP Records. Search for n!3-59049.</a>
%H A265201 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>
%e A265201 19!3 - 3^10 = 19*16*13*10*7*4*1 - 59049 = 1047511 is prime, so 19 is in the sequence.
%t A265201 MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
%t A265201 Select[Range[17, 50000], PrimeQ[MultiFactorial[#, 3] - 3^10] &]
%o A265201 (PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
%o A265201 for(n=1, 1e4, if(ispseudoprime(tf(n) - 3^10), print1(n , ", "))) \\ _Altug Alkan_, Dec 04 2015
%Y A265201 Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145.
%K A265201 hard,more,nonn
%O A265201 1,1
%A A265201 _Robert Price_, Dec 04 2015