# Recursive Digit Sum

**Number Theory**Level 4

Given a positive integer \(n\), let \(S(n)\) denote the digit sum of \(n\). Consider the sequence of numbers given by

\[ \begin{cases} n_1 = S(n) \\ n_k = S(n_{k-1} ) & k \geq 2 \\ \end{cases}\]

For how many positive integers \(n \le 2013\) does the sequence \( \{ n_k \} \) contain the number \(9\)?