# Induction or function? (corrected)

Algebra Level 5

Let $$f$$ be a function from $$\mathbb{N}$$ to $$\mathbb{N}$$ such that

$$\quad 1.~ f(1)=0$$
$$\quad 2.~ f(2n)=2f(n)+1$$
$$\quad 3.~ f(2n+1)=2f(n).$$

Find the smallest value of $$n$$ such that $$f(n)=1994$$.

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