Induction or function? (corrected)

Algebra Level 4

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

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

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

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

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