BALTIC-WAY 2017 Problem 19

For an integer $n \geq 1$ let $a(n)$ denote the total number of carries which arise when adding 2017 and $n \cdot 2017$. The first few values are given by $a(1)=1, a(2)=1, a(3)=0$, which can be seen from the following:

Prove that

$$a(1)+a(2)+\ldots+a\left(10^{2017}-2\right)+a\left(10^{2017}-1\right)=10 \cdot \frac{10^{2017}-1}{9}$$