The 421 Loop

A Math-magical Loop Pick a whole number and enter it into your calculator.

    If it is even, divide by 2. If it is odd, multiply by 3 and add 1.
    Repeat the process with the new number over and over. What happens?
    The sequence always ends in the "loop": 4.....2.....1.....4.....2.....1...

Let’s illustrate with an Example:

Start with 17 17 is odd, so we multiply by 3 and add 1. We get 52. (17x3=51+1=52) 52 is even, so we divide by 2. We get 26. (52 / 2 = 26) 26 is also even, so we divide by 2 again and get 13. 13 is odd, so we multiply by 3 and add 1. We get 40. (13x3=39+1=40) 40 is even, so we divide by 2. We get 20. (40 / 2 = 20) 20 is even, so we divide by 2 and get 10. 10 is also even so we divide by 2 again and get 5. 5 is odd so we multiply by 3 and add 1. We get 16. 16 is even, so we divide by 2 and get 8. 8 is also even so we divide by 2 again and get 4. 4 is even so we divide by 2. We get 2. 2 is even, so we divide by 1 and get 1. 1 is odd, so we multiply by 3 and add 1. We get 4. 4 is even so we divide by 2. We get 2. And so we begin the loop 4.....2.....1.....4.....2.....1...