PUMaC 2011 Team Sudoku Problem 5

For any n \in \mathbb{N} such that 1<n<10, define the sequence X_{n, 1}, X_{n, 2}, \ldots by X_{n, 1}=n, and for r \geq 2, X_{n, r} is smallest number k \in \mathbb{N} larger than X_{n, r-1} such that k and the sum of digits of k are both powers of n. For instance, X_{3,1}=3, X_{3,2}=9, X_{3,3}=27, and so on. Concatenate X_{2,2} with X_{2,4}, and write down the answer.