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Numbers whose factorial has '68' as its final two digits before the trailing zeros.
1

%I #15 Jun 22 2021 01:03:16

%S 11,15,22,27,39,70,73,89,106,149,184,191,197,221,229,274,295,298,310,

%T 318,329,354,379,430,467,474,492,505,514,540,611,655,702,706,762,810,

%U 818,832,845,848

%N Numbers whose factorial has '68' as its final two digits before the trailing zeros.

%H Charles R Greathouse IV, <a href="/A045564/b045564.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 f2nzdQ[n_] := Mod[n!/10^IntegerExponent[n!, 10], 100] == 68; Select[ Range[ 900],f2nzdQ] (* _Harvey P. Dale_, Aug 14 2017 *)

%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)==68 \\ _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==68 \\ _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==68,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_