# Induction or function? (corrected)

Algebra Level 4

Let $$f$$ be a function from $$\mathbb{Z}^+$$ to $$\mathbb{Z}^*$$ such that

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

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

Notation: $$\mathbb Z^+$$ denotes the set of positive integers, and $$\mathbb{Z}^*$$ denotes the set of non-negative integers.

×