pick a positive integer.
1. if it is even, divide by 2
2. if it is odd, multiply by 3 and add 1
3. repeat steps 1 and 2.
eventually, you will reach the value 1, in which case you go into the loop 4, 2, 1.
for example, starting at 3, you get 10, then 5, 16, 8, 4, 2, 1.
starting at...