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%I #16 Jun 21 2021 06:03:22
%S 7,28,56,64,124,138,152,164,214,233,239,244,263,283,294,304,358,364,
%T 369,381,459,466,484,488,491,524,529,532,561,604,646,703,737,804,830,
%U 893,905,952,956,977,980,1008,1019,1034,1036,1041,1050,1051,1086,1093
%N Numbers whose factorial has '04' as its final two digits before the trailing zeros.
%H Charles R Greathouse IV, <a href="/A045551/b045551.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 f[ n_Integer, m_Integer ] := (c = 0; p = 1; While[ d = Floor[ n/5^p ]; d > 0, c = c + d; p++ ]; Mod[ n!/10^c, m ] ); Select[ Range[ 250 ], f[ #, 100 ] == 4 & ]
%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)==4 \\ _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==4 \\ _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==4,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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