%I #13 Jun 22 2021 01:02:06

%S 8,19,35,74,85,97,118,145,148,180,203,225,226,270,273,287,299,306,314,

%T 325,326,337,350,351,375,376,434,441,447,457,470,473,482,509,510,516,

%U 533,544,627,659,661,666,711,718,747,806,814,842,849

%N Numbers whose factorial has '32' as its final two digits before the trailing zeros.

%H Charles R Greathouse IV, <a href="/A045557/b045557.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)==32 \\ _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==32 \\ _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==32,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_