Step 4: What are we counting?
So, what are those numbers? They seem pretty random! To answer that, we need to know a bit more about the Collatz conjecture. It claims that if you take a whole number bigger than 1 and do the following:
- If the number is even, halve it.
- If the number is odd, multiply it by 3 and add 1.
- Repeat!
then eventually You might like to try this for the first few numbers, starting from 2. at 1.
What we’re doing is counting What if the conjecture was false and our program didn’t stop? Fortunately, we already know that won’t happen until at least a very large starting number, as this has already been tried! we have to repeat the above steps to reach 1, starting at 2, then 3, then 4, and so on for ten numbers (range(10)), which takes us up to 11.
We can now get a fairly good idea of what the second part of the program is doing.