a=1.002004008016032064128256
=1+(2/1000)+(2/1000)^2+...+(2/1000)^7＜1+(2/1000)+(2/1000)^2+...
=1/(1-(2/1000))=1000/998=1+e,e=2/998

a^4＜(1+e)^4=1+4e+6e^2+4e^3+e^4＜1+5e
a^16＜(1+5e)^4＜1+4*5e+6*(5e)^2+...＜1+21e
a^64＜(1+21e)^4＜1+85e
a^256＜(1+85e)^4＜1+341e=1+341*2/998＜1+(682+2)/(998+2)=1.684＜√3