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

1,1

Comments

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

a(46) > 50000.

Terms > 61 correspond to probable primes.

Links

Table of n, a(n) for n=1..45.

Henri & Renaud Lifchitz, PRP Records. Search for n!3+19683.

Joe McLean, Interesting Sources of Probable Primes

OpenPFGW Project, Primality Tester

Example

11!3 + 3^9 = 11*8*5*2 + 19683 = 20563 is prime, so 11 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] + 3^9] &]

Prog

(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

Crossrefs

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

Sequence in context: A310971 A310972 A246357 * A235382 A287201 A310973

Adjacent sequences: A265375 A265376 A265377 * A265379 A265380 A265381

Keyword

nonn,more

Author

Robert Price, Dec 07 2015

Status

approved