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Numbers whose factorial has '72' as its final two digits before the trailing zeros.
1

%I #14 Jun 22 2021 01:03:41

%S 6,40,53,62,67,109,113,116,146,162,174,200,201,212,237,271,278,305,

%T 362,392,438,471,495,498,531,583,594,709,716,735,740,770,773,805,828,

%U 850,851,882,967,974,999,1000,1001,1059,1066,1072,1082,1095,1098,1107,1143

%N Numbers whose factorial has '72' as its final two digits before the trailing zeros.

%H Charles R Greathouse IV, <a href="/A045565/b045565.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)==72 \\ _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==72 \\ _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==72,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