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A267382
Numbers n such that n!3 - 3^7 is prime, where n!3 = n!!! is a triple factorial number (A007661).
1
13, 14, 16, 19, 22, 23, 26, 38, 64, 104, 137, 203, 296, 346, 347, 379, 481, 568, 899, 1162, 1603, 2614, 5698, 5846, 9253, 9565, 9848, 10406, 16051, 18377, 23110, 26026, 26120, 28994
OFFSET
1,1
COMMENTS
Corresponding primes are: 1453, 10133, 56053, 1104373, 24342133, 2504900213, 3091650738173813, ... .
a(35) > 50000.
Terms > 26 correspond to probable primes.
EXAMPLE
13!3 - 3^7 = 13*10*7*4 - 2187 = 1453 is prime, so 13 is in the sequence.
MATHEMATICA
MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[13, 50000], PrimeQ[MultiFactorial[#, 3] - 3^7] &]
Select[Range[12, 6000], PrimeQ[Times@@Range[#, 1, -3]-2187]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Aug 14 2024 *)
KEYWORD
nonn,more
AUTHOR
Robert Price, Jan 13 2016
STATUS
approved