%I #18 Jun 22 2021 01:03:48
%S 45,48,65,79,107,127,175,176,209,216,247,252,285,303,312,317,335,347,
%T 372,386,390,397,405,429,452,456,481,528,603,649,688,707,720,723,729,
%U 755,764,784,786,791,803,812,817,836,843
%N Numbers whose factorial has '76' as its final two digits before the trailing zeros.
%H Harvey P. Dale, <a href="/A045566/b045566.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%t Select[Range[5,900],Take[Flatten[Most[Split[IntegerDigits[#!]]]],-2]=={7,6}&] (* _Harvey P. Dale_, Apr 04 2013 *)
%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)==76 \\ _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==76 && n>1 \\ _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==76,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_