A natural number \(n\) is written on the whiteboard. You start with the number \(1\) on a piece of paper. You may perform two operations: “double up” (multiply the number on your paper by \(2\)) and “increase by \(1\)” (add \(1\) to the number on your paper).
What is the smallest number of operations needed to obtain \(n\) starting from \(1\)?