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.

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