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%I #18 Jun 22 2021 01:04:16
%S 17,46,60,68,120,123,160,210,222,235,240,290,300,301,360,365,393,455,
%T 477,480,520,523,525,526,542,600,601,628,686,721,752,800,801,834,841,
%U 872,881,909,911,916,961,968,984,988,991,1011,1015,1022,1030,1054,1077
%N Numbers whose factorial has '96' as its final two digits before the trailing zeros.
%H Harvey P. Dale, <a href="/A045570/b045570.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[5,1100],Flatten[Take[Most[Split[IntegerDigits[#!]]],-2]] == {9,6}&] (* _Harvey P. Dale_, Apr 08 2012 *)
%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)==96 \\ _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==96 \\ _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==96,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_
%E More terms from _Robert G. Wilson v_, Dec 14 2000
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