%I #15 Jun 22 2021 01:04:09

%S 84,91,110,115,181,189,217,224,228,302,308,319,328,353,378,404,407,

%T 435,443,518,527,539,554,589,602,605,630,639,663,668,672,675,676,713,

%U 715,736,757,775,776,792,802,808,819

%N Numbers whose factorial has '92' as its final two digits before the trailing zeros.

%H Charles R Greathouse IV, <a href="/A045569/b045569.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%t fndQ[n_]:=Module[{f=n!},Take[Drop[IntegerDigits[f],-IntegerExponent[ f,10]],-2] == {9,2}]; Select[Range[5,900],fndQ] (* _Harvey P. Dale_, Sep 26 2016 *)

%o (PARI) last(n,k)=if(n*8\9-1<k, n=n!; return(n/10^valuation(n,10)%10^k)); my(m=Mod(1,5^k)); for(i=2,n,m*=i/10^valuation(i,5));lift(chinese(m, Mod(0,2^k))) \\ Gives the last k decimal digits of n!.

%o is(n)=last(n,2)==92 \\ _Charles R Greathouse IV_, Oct 22 2014

%o (PARI) is(n)=my(m=Mod(1,25)); for(i=2,n, m*=i/10^valuation(i,5)); m==92 \\ _Charles R Greathouse IV_, Oct 22 2014

%o (PARI) v=List();m=Mod(1,25);for(n=2,1e6,m*=n/10^valuation(n,5);if(m==92,listput(v,n);if(#v==100, return(Vec(v))))) \\ _Charles R Greathouse IV_, Oct 22 2014

%K nonn,base

%O 1,1

%A _Jeff Burch_