A264867 Numbers n such that n!3 + 3^8 is prime, where n!3 = n!!! is a triple factorial number (A007661).

2, 5, 10, 26, 34, 35, 37, 59, 68, 76, 104, 106, 188, 193, 242, 278, 287, 290, 572, 772, 773, 1304, 2384, 2716, 3715, 4562, 6706, 11489, 11711, 21602, 24295, 24775, 27224, 29935, 37856

Offset

1,1

Comments

Corresponding primes are 6563, 6571, 6841, 2504908961, 17961239302561, 81359229958561, 664565853958561, ...

Terms > 68 correspond to probable primes.

a(36) > 50000.

Links

Table of n, a(n) for n=1..35.

Henri & Renaud Lifchitz, PRP Records. Search for n!3+3^8

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

10!3 + 3^4 = 10*7*4*1 + 6561 = 6841 is prime, so 10 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[800], PrimeQ[6561+Times@@Range[#, 1, -3]]&] (* Harvey P. Dale, Mar 08 2023 *)

Prog

(PARI) is(n)=ispseudoprime(n!!! + 3^8) \\ Anders Hellström, Nov 27 2015
(PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^8), print1(n , ", "))) \\  Altug Alkan, Dec 03 2015

Crossrefs

Cf. A007661, A037082, A084438, A243078.

Sequence in context: A297860 A002094 A212709 * A354832 A115725 A305577

Adjacent sequences: A264864 A264865 A264866 * A264868 A264869 A264870

Keyword

nonn,more

Author

Robert Price, Nov 26 2015

Status

approved