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Numbers whose factorial has '44' as its final two digits before the trailing zeros.
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%I #13 Jun 22 2021 01:02:22

%S 21,78,112,134,135,141,155,182,196,202,206,259,260,266,320,323,330,

%T 413,418,422,428,437,442,463,465,485,490,517,545,548,559,566,572,579,

%U 620,623,650,651,667,680,728,768,781,820,823,833,844

%N Numbers whose factorial has '44' as its final two digits before the trailing zeros.

%H Charles R Greathouse IV, <a href="/A045559/b045559.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)==44 \\ _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==44 \\ _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==44,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_