Recursive Function

Let f:NN f : \mathbb{N} \rightarrow \mathbb{N} be a function defined as follows:

f(n)={1n=1,f(k)n=2k,f(k)+1n=2k+1. f(n) = \begin{cases} 1 & n=1 ,\\ f(k) & n = 2k, \\ f(k) + 1 & n = 2k+ 1. \\ \end{cases} Let AA be the maximum value of f(n)f(n) on 1n2013 1 \leq n \leq 2013 . Calculate the number of values of nn with 1n2013 1 \leq n \leq 2013 such that f(n)=A f(n) = A .

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