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A267029
Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).
1
16, 17, 34, 38, 49, 62, 74, 97, 125, 137, 146, 178, 188, 235, 664, 863, 916, 1988, 2059, 2837, 5353, 5489, 7483, 9344, 12631, 13796, 17122, 23134, 30409, 33077
OFFSET
1,1
COMMENTS
Corresponding primes are 38557, 189757, 17961239276317, 3091650738156317, ... .
a(31) > 50000.
EXAMPLE
16!3 - 3^9 = 16*13*10*7*4*1 - 19683 = 58240 - 19683 = 38557 is prime, so 16 is in the sequence.
MATHEMATICA
MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[15, 50000], PrimeQ[MultiFactorial[#, 3] - 3^9] &]
Select[Range[12, 33100], PrimeQ[Times@@Range[#, 1, -3]-19683]&] (* Harvey P. Dale, Jan 25 2021 *)
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Jan 09 2016
STATUS
approved