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

Author

Robert Price, Nov 26 2015

Keywords

• nonn
• more

Comments

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

Terms > 68 correspond to probable primes.

a(36) > 50000.

Examples

			10!3 + 3^4 = 10*7*4*1 + 6561 = 6841 is prime, so 10 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!3+3^8
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007661, A037082, A084438, A243078.

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[800],PrimeQ[6561+Times@@Range[#,1,-3]]&] (* Harvey P. Dale, Mar 08 2023 *)

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