KZ-MO 2004 Problem 6

The sequence of integers $a_1$ , $a_2$ , $\dots$ is defined as follows: $a_1 = 1$ and $n> 1$ , $a_ {n + 1}$ is the smallest integer greater than $a_n$ and such, that $a_i + a_j \neq 3a_k$ for any $i, j$ and $k$ from $\{1, 2, \dots, n + 1 \}$ are not necessarily different. Define $a_ {2004}$ .