The Collatz sequence is also called the "3n + 1" sequence because it is generated by starting with any positive number and following just two simple rules: If it's even, divide it by two, and if it's odd, triple it and add one. Hence, "3n + 1." Follow those two rules over and over, and the conjecture states that, regardless of the starting number, you will always eventually reach the number one.

For example, start with the number seven. It's an odd number, so you give it the old 3n + 1 treatment, which equals 22. That's an even number, which means you've got to cut it in half, which gives us 11. Here's the calculation for rest of the sequence:

**11 x 3 = 33 + 1 = 34**

34 / 2 = 17

17 x 3 = 51 + 1 = 52

52 / 2 = 26

26 / 2 = 13

13 x 3 = 39 + 1 = 40

40 / 2 = 20

20 / 2 = 10

10 / 2 = 5

5 x 3 = 15 + 1 = 16

16 / 2 = 8

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1

So, if you start with the number seven, the Collatz sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. If you do it again from the number one, an odd number, you multiply by three and add one. From there you get four, which quickly reduces back to one. This begins the loop that never ends.