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Numbers n such that n!10-1 is prime.
8

%I #25 Nov 12 2019 11:34:32

%S 3,4,6,8,12,20,40,48,60,62,70,84,88,168,240,258,372,760,932,1010,2110,

%T 2464,2490,2702,3180,4744,6024,8858,9060,10322,13382,15778,19322,

%U 22372,22928,25344,28050,40604,42282,45884,52428,58250,81220,93612,108650

%N Numbers n such that n!10-1 is prime.

%C n!10 = product( n-10k, 0 <= k < n/10 ).

%C See also links in A156165.

%C a(1)-a(40) are proved prime by deterministic tests of pfgw. - _Robert Price_, Jun 11 2012

%C a(41) > 50000. - _Robert Price_, Jun 11 2012

%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.

%H Ken Davis, <a href="http://mfprimes.free-dc.org/mfdata/f10m.html">Results for n!10-1.</a>

%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];

%t Select[Range[1000], PrimeQ[MultiFactorial[#, 10] - 1] & ] (* _Robert Price_, Apr 19 2019 *)

%o (PARI) for(n=0,9999,isprime(prod(i=0,(n-2)\10,n-10*i)-1)& print1(n","))

%Y Cf. A204657, A204659, A204660, A204661, A204662, A204663, A204664, A156165, A156167, A085150, A085148, A085146, A037083, A080778, A002981.

%K nonn,hard

%O 1,1

%A _M. F. Hasler_, Jan 17 2012

%E a(26)-a(40) from _Robert Price_, Jun 11 2012

%E a(41)-a(45) from Ken Davis link entered by _Robert Price_, Apr 19 2019