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First 9-free digit in the fractional part of the decimal expansion of (1/10^n)^(1/10^n).
0

%I #8 Oct 01 2013 17:58:11

%S 0,7,5,3,0,8,8,8,8,7,7,7,7,7,6,6,6,6,5,5,5,5,4,4,4,4,4,3,3,3,3,2,2,2,

%T 2,1,1,1,1,1,0,0,0,0,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%U 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7

%N First 9-free digit in the fractional part of the decimal expansion of (1/10^n)^(1/10^n).

%e (1/10^0)^(1/10^0) =1^1 = 1.000000.. 9-free = 0

%e (1/10^1)^(1/10^1) =(1/10)^(1/10) = 0.794328.. = 7

%e (1/10^2)^(1/10^2) =(1/100)^(1/100) = 0.954992.. = 5

%o (PARI) zerotozero(n) = { local(x,y,z,v,j); for(x=0,n, y=10^x; v=(1./y)^(1/y); z=Vec(Str(v)); for(j=3,n, if(z[j]<>"9", print1(z[j]",");break) ) ) }

%K nonn,base

%O 0,2

%A _Cino Hilliard_, May 06 2005