1. The desired number is equal to $(9+1)+(99+1)+\ldots+(\underbrace{99 \ldots 9}_{2016 \text { times }}+1)+1=$

$=10+10^{2}+\cdots+10^{2016}+1=\underbrace{11 \ldots 1}_{2017 \text { times }}$.
Answer: $\underbrace{11 \ldots 1}_{2017 \text { times }}$.