A265201 Numbers n such that n!!! - 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661)..

19, 20, 22, 26, 41, 55, 56, 152, 155, 316, 347, 383, 500, 556, 646, 656, 748, 976, 1433, 2213, 2680, 2911, 3373, 4799, 4964, 7189, 8798, 9871, 14069, 14627, 16657, 20230, 24137, 24430, 28331, 36313, 41522, 43031, 46072, 47719

Offset

1,1

Comments

Corresponding primes are 1047511, 4129751, 24285271, 2504843351, 126757680265156951, ... .

a(41) > 50000.

Links

Table of n, a(n) for n=1..40.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-59049.

Joe McLean, Interesting Sources of Probable Primes

Example

19!3 - 3^10 = 19*16*13*10*7*4*1 - 59049 = 1047511 is prime, so 19 is in the sequence.

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[17, 50000], PrimeQ[MultiFactorial[#, 3] - 3^10] &]

Prog

(PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
for(n=1, 1e4, if(ispseudoprime(tf(n) - 3^10), print1(n , ", "))) \\ Altug Alkan, Dec 04 2015

Crossrefs

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145.

Sequence in context: A289469 A093680 A007640 * A274340 A241849 A054304

Adjacent sequences: A265198 A265199 A265200 * A265202 A265203 A265204

Keyword

hard,more,nonn

Author

Robert Price, Dec 04 2015

Status

approved