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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