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

1,1

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.

Links

Table of n, a(n) for n=1..39.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-6561.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

16!3 - 3^8 = 16*13*10*7*4*1 - 6561 = 51679 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[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 *)

Prog

(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

Crossrefs

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

Sequence in context: A145449 A138599 A258265 * A007636 A241751 A374559

Adjacent sequences: A261341 A261342 A261343 * A261345 A261346 A261347

Keyword

nonn,more

Author

Robert Price, Nov 18 2015

Status

approved