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%I #13 Nov 08 2017 07:43:30
%S 68,88,91,118,131,151,157,194,203,424,602,772,832,884,947,1309,1463,
%T 2246,3304,4043,5725,6683,9344,10969,11026,11735,13664,14857,18529,
%U 21676,28217,28793,29605,33206,41182,43777,49936
%N Numbers n such that n!!! - 3^n is prime.
%C n!!! is the triple factorial sometimes written n!3.
%C If taking absolute values: 1,2,5,8,13,26,29,31,41,43,44,46,56,59 would also be in this sequence.
%C a(38) > 50000.
%e 68 is in the sequence because 68!!!-3^68=350834017732995704466119535768239 is prime.
%t MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
%t Select[Range[0, 100], MultiFactorial[#, 3] - 3^# > 0 && PrimeQ[MultiFactorial[#, 3] - 3^#] &]
%Y Cf. A007661, A124248, A124249.
%K nonn
%O 1,1
%A _Robert Price_, Aug 14 2015