

A265378


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


1



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
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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, (n1)\3, n3*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



