# 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 $$2$$?

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