Answer:
Step-by-step explanation:
The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.
Simply put it says
- if a number is even, divide by 2
- If a number is odd, multiply by 3 and add1. or 3x + 1
- The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.
Try 5
- It's odd so triple it and add 1. You get 16
- 16 is even. Divide by 2. You get 8
- 8 is even. Divide by 2. You get 4
- 4 is even. Divide by 2. You get 2
- 2 is even. Divide by 2. You get 1
- 1 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.
Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.
- Take 15
- It's odd. Triple it and add 1. That gives 46.
- 46 is even. Divide by 2
- 23 which is odd. Triple it and add 1 = 70
- 70 is even. Divide by 2. 35
- 35 is odd. Triple and add 1. 106 which is even
- 53 which is odd. Triple it and add 1. You get 160
- 160 is even. Divide by 2. You get 80
- 80 is even Divide by 2. You get 40
- 40 is even. Divide by 2. You get 20
- 20 is even. Divide by 2. You get 10
- 10 is even. Divide by 2. You get 5
- 5 is odd. Triple it and add 1. You get 16
- 16 is even. Divide by 2. You get 8
- 8 is even. Divide by 2. You get 4
- 4 is even. Divide by 2.. You get 2.
- 2 is even. Divide by 2. You get 1
- 1 is odd and you are in the loop because you get 4 which you have already done.
