A265378 Numbers n such that n!3 + 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

4, 8, 10, 11, 14, 17, 20, 22, 29, 32, 44, 56, 61, 173, 202, 211, 215, 241, 388, 410, 416, 569, 583, 680, 823, 964, 1271, 1732, 2309, 2335, 2404, 2765, 3019, 3047, 4670, 5209, 6320, 6817, 7531, 9923, 11243, 14912, 17969, 21193, 28940

Offset: 1

Author

Robert Price, Dec 07 2015

Keywords

• nonn
• more

Comments

Corresponding primes are: 19687, 19763, 19963, 20563, 32003, 229123, 4208483, 24364003, 72642189283, ...

a(46) > 50000.

Terms > 61 correspond to probable primes.

Examples

			11!3 + 3^9 = 11*8*5*2 + 19683 = 20563 is prime, so 11 is in the sequence.
		

Links

• Henri & Renaud Lifchitz, PRP Records. Search for n!3+19683.
• Joe McLean, Interesting Sources of Probable Primes
• OpenPFGW Project, Primality Tester

Crossrefs

Cf. A007661, A037082, A084438, A123910, A242994, A261145, A265200.

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] + 3^9] &]

PARI

tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) + 3^9), print1(n , ", "))) \\ Altug Alkan, Dec 07 2015