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%I #14 Oct 19 2023 11:26:47
%S 8,10,11,13,16,19,20,22,37,38,47,73,92,94,100,218,241,284,482,541,736,
%T 787,829,916,1147,1312,1856,1928,2035,3134,4958,5503,8042,16898,16987,
%U 24548,25076,35086
%N Numbers n such that n!3 + 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C Corresponding primes are: 2267, 2467, 3067, 5827, 60427, 1108747, 4190987, 24346507, 664565853954187, ...
%C a(39) > 50000.
%C Terms > 38 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+2187&action=Search">PRP Records. Search for n!3+2187.</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 + 3^7 = 11*8*5*2 + 2187 = 3067 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] + 3^7] &]
%t Select[Range[35100],PrimeQ[Times@@Range[#,1,-3]+2187]&] (* _Harvey P. Dale_, Oct 19 2023 *)
%o (PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
%o for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^7), print1(n , ", "))) \\ _Altug Alkan_, Dec 04 2015
%Y Cf. A007661, A037082, A084438, A123910, A242994, A261145.
%K nonn,more
%O 1,1
%A _Robert Price_, Dec 04 2015
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