%I #13 Jun 22 2021 01:01:35
%S 5,14,38,43,47,50,51,88,90,111,129,153,242,254,275,276,292,367,387,
%T 420,423,436,454,496,513,530,570,573,577,581,608,614,619,633,644,660,
%U 699,710,722,743,771,787,799,825,826,837
%N Numbers whose factorial has '12' as its final two digits before the trailing zeros.
%H Charles R Greathouse IV, <a href="/A045553/b045553.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>
%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)==12 \\ _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==12 \\ _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==12,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_