This simple page will let you explore the sequence that is given by the following simple rule:
- If the previous number is even, then the next number is half the previous number
- If the previous number is odd, then the next number is one more than triple the previous number
In math-ese, this translates into:
- an + 1 = an/2, if an is even
- an + 1 = 3an + 1, if an is odd
The rules above give very different sequences if we use different starting numbers. Try some of the following starting numbers:
Try it out!
Why does the computer stop when it gets to 1? What would the sequence be that starts at 1?
Can you predict how long the sequence will be if you know the starting number?
Will the sequence always reach 1? (This question is known in mathematically knowledgable cirlces as the Collatz Conjecture.)