Posted by **Arnau** on Thursday, May 2, 2013 at 5:48am.

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

n₁ = S(n)

nk = S(nk−1)k≥2

For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?

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