In 1937 Lothar Collatz proposed the 3n+1 conjecture (known by a long list of aliases), is stated as follows.

First, we define the function on the set of positive integers:

If the number is even, divide it by two: .

If the number is odd, triple it and add one: .

In modular arithmetic notation, define the function as follows:

, and . Believe it or not, this is the restriction to the positive integers of the complex-valued map .

The **3n+1 conjecture** is: *The sequence*

*will eventually reach the number 1, regardless of which positive integer is chosen initially.*

This is still unsolved, though a lot of people have worked on it. For a recent survey of results, see the paper by Chamberland.

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