f(0)=0, f(1)=1
f(1/2)+f(1/2)= 1, then f(1/2)= 1/2
f(1/5)= (1/2) f(1)= 1/2, then f(4/5)= 1/2
while x1< x2, f(x1)<= f(x2) , so f(x)= 1/2 for x=1/5~4/5
then
f(x)= 1/4 for x= 1/25~4/25
f(x)= 1/8 for x= 1/125~4/125
f(x)= 1/16 for x= 1/625~4/625
f(x)= 1/32 for x= 1/3125~4/3125
so, f(1/2013)= 1/32