A045568 - OEIS

%I #13 Jun 22 2021 01:04:01

%S 9,10,16,31,54,83,94,125,126,171,186,232,250,251,279,282,313,357,412,

%T 424,450,451,462,478,534,536,541,574,586,593,610,615,636,640,647,652,

%U 664,695,698,714,731,753,795,798,813,829

%N Numbers whose factorial has '88' as its final two digits before the trailing zeros.

%H Charles R Greathouse IV, <a href="/A045568/b045568.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)==88 \\ _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==88 \\ _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==88,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_