A204661 Numbers n such that n!8+1 is prime (for n!8 see A114800).

0, 1, 2, 4, 6, 28, 30, 46, 60, 72, 86, 90, 112, 154, 162, 206, 280, 354, 400, 512, 606, 614, 678, 790, 938, 1054, 1092, 1148, 1582, 1788, 2088, 2206, 2598, 2912, 3672, 4642, 6272, 6428, 7084, 7604, 8580, 9464, 12762, 18386, 24910, 30448, 31696, 40288, 41682, 45730

Offset: 1

Author

M. F. Hasler, Jan 17 2012

Keywords

• nonn
• hard

Comments

n!8 = A114800(n).

No other terms < 50000. - Robert Price, Jul 29 2012

Links

• Ken Davis, Status of Search for Multifactorial Primes.
• Ken Davis, Results for n!8+1.

Crossrefs

Cf. A204657, A204658, A204659, A204660, 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[0, 1000], PrimeQ[MultiFactorial[#, 8] + 1] & ] (* Robert Price, Apr 19 2019 *)
Select[Range[0,46000],PrimeQ[Times@@Range[#,1,-8]+1]&] (* Harvey P. Dale, Apr 12 2022 *)

PARI

for(n=0,9999,isprime(prod(i=0,(n-2)\8,n-8*i)+1)& print1(n","))

Extensions

a(35)-a(50) from Robert Price, Jul 29 2012