Splitting the plane
Suppose we have \(n\) lines in a plane. Every pair of lines intersect such that no three lines intersect in a common point. Let \(A_n\) be the number of regions in the plane divided into by these \(n\) lines. How many positive integers \(n \leq 10^6 \) are there such that \(A_n\) is a power of \(2\)?