PL-OM 1993 Problem 3

Denote $g(k)$ as the greatest odd divisor of $k$ . Put $f(k) = \dfrac{k}{2} + \dfrac{k}{g(k)}$ for $k$ even, and $2^{(k+1)/2}$ for $k$ odd. Define the sequence $x_1, x_2, x_3, ...$ by $x_1 = 1$ , $x_{n+1} = f(x_n)$ . Find $n$ such that $x_n = 800$ .