A204659 Numbers n such that n!9-1 is prime.

3, 4, 6, 8, 15, 20, 23, 27, 30, 44, 51, 62, 80, 90, 95, 114, 129, 138, 150, 152, 156, 182, 201, 216, 293, 332, 342, 393, 411, 414, 419, 525, 668, 743, 800, 972, 1034, 1266, 1785, 1869, 2777, 3561, 3780, 4106, 4328, 4428, 4556, 4574, 4629, 5001, 5397, 6315

Offset: 1

Author

M. F. Hasler, Jan 17 2012

Keywords

• nonn
• hard

Comments

n!9 = A114806(n).

a(74) > 50000. - Robert Price, Jun 14 2012

a(1)-a(73) are proved prime by the deterministic test of pfgw. - Robert Price, Jun 14 2012

Links

• Robert Price, Table of n, a(n) for n = 1..81
• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!9-1.

Crossrefs

Cf. A204657, A204658, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

Programs

Mathematica

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], PrimeQ[MultiFactorial[#, 9] - 1] & ] (* Robert Price, Apr 19 2019 *)

PARI

for(n=0,9999,isprime(prod(i=0,(n-2)\9,n-9*i)-1)& print1(n","))

Extensions

a(47)-a(73) from Robert Price, Jun 14 2012

Extended b-file adding a(74)-a(81) using data from Ken Davis link by Robert Price, Apr 19 2019