The Collatz sequence in Python.

The program

Press Run to see what it prints. Change anything you like, then run it again.

n = 27
steps = 0
highest = n
while n != 1:
    if n % 2 == 0:
        n = n // 2
    else:
        n = 3 * n + 1
    steps = steps + 1
    if n > highest:
        highest = n
print("Steps:", steps)
print("Highest number reached:", highest)

Steps: 111
Highest number reached: 9232

How it works

1. The Collatz conjecture says that this process always ends at 1, whichever number you start with. Nobody has proved it, even though computers have checked huge numbers.
2. Starting at 27 takes 111 steps and climbs as high as 9,232 before falling back to 1.
3. The program counts the steps and remembers the highest value. Try other starting numbers.

Try this

• Try a starting number from 1 to 30 and see which takes the longest.
• Print the whole sequence.
• Use a for loop to find the starting number below 100 with the most steps.

Stuck on an error? Read how to debug Python.