A261344 Numbers n such that n!3 - 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

16, 17, 20, 25, 26, 35, 37, 47, 88, 94, 125, 127, 134, 326, 328, 368, 398, 425, 698, 700, 734, 1303, 1427, 2011, 2542, 2699, 3938, 4214, 5137, 6314, 8669, 9041, 12494, 13520, 14609, 23732, 41399, 43867, 49471

Offset: 1

Author

Robert Price, Nov 18 2015

Keywords

• nonn
• more

Comments

n=5 and n=8 produce values (-6551 and -6481) whose absolute value is a prime.

Corresponding primes are: 51679, 202879, 4182239, 608601439, 2504895839, ...

a(40) > 50000.

Terms > 26 correspond to probable primes.

Examples

			16!3 - 3^8 = 16*13*10*7*4*1 - 6561 = 51679 is prime, so 16 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!3-6561.
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] - 3^8] &]
Select[Range[14,800],PrimeQ[Times@@Range[#,1,-3]-6561]&] (* The program generates the first 21 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Apr 27 2022 *)

PARI

for(n=1, 1e3, if(ispseudoprime(prod(i=0, floor((n-1)/3), n-3*i) - 3^8), print1(n, ", "))) \\ Altug Alkan, Nov 18 2015