Skip to content

The Collatz-Conjecture

The Problem

This is a famous and not yet fully solved problem in mathmatics. Here are the rules:

  • Start with any positive integer number x
  • If x is even, assign x ← x/2
  • If x is odd, assign x ← 3x + 1

Eventually your sequence will end up in the loop 4 → 2 → 1 → 4 … (The unsolved part is that there is no proof yet that this always happens.)

Now you!

Implement a loop that generates and prints the sequence for any given positive starting number. You can either set the starting value in a variable at the beginning of your program or read it from a user input. The loop should stop if x reaches one of the three numbers (4, 2, or 1) that are known to form an endless cycle.

Example Output:

Starting Value: 5
4 - 2- 1, Yeah, I know...

To check if a number is even, the modulo-operator (written as % in Python) might be very helpful. It calculates the remainder of a whole-number division.

For example 13 // 3 == 4and since 4 * 3 == 12 that leaves a reminder of 1 to get to the original 13. Therefore, 13 % 3 == 1.