BALTIC-WAY 2005 Problem 1

Let $a_{0}$ be a positive integer. Define the sequence $a_{n}, n \geq 0$, as follows: If

$$a_{n}=\sum_{i=0}^{j} c_{i} 10^{i}$$

where $c_{i}$ are integers with $0 \leq c_{i} \leq 9$, then

$$a_{n+1}=c_{0}^{2005}+c_{1}^{2005}+\cdots+c_{j}^{2005} .$$

Is it possible to choose $a_{0}$ so that all the terms in the sequence are distinct?