Collatz Conjecture - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim

Collatz Conjecture

Main Concept

The Collatz Conjecture, also known as the 3n+1 Conjecture, states that if you choose any natural number and repeatedly perform a "Half Or Triple Plus One" (HOTPO) procedure, you will always eventually reach 1.


HOTPO: Choose an integer n greater than 0. Then:


if n is even, divide it by 2 to obtain n2


if n is odd, multiply it by 3 and add 1 to obtain 3n+1 


Now, apply this same process to the resulting number, and keep repeating this process indefinitely. You end up with a sequence of positive integers:


7  3×7+1= 22  22÷2 = 11  3×11+1=34  34÷2 = 17 ...


In the resulting sequence, sometimes the numbers go up and sometimes they go down, and it can be hard to predict whether the number even a few iterations away will be higher or lower than the current number. If the conjecture is right though, eventually the number sequence always decreases to 1.


Enter a natural number in the text box below and click the button to see the next calculation in the "Half or Triple Plus One" procedure. Do your calculations always eventually reach the number 1?


More MathApps