the Collatz conjecture

From Wikipedia:

Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called “Half Or Triple Plus One”, or HOTPO[6]) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1.

def collatz(n,itmax=10000):
    it = 0
    while not n==1 and it<itmax:
       it += 1
       if n % 2 == 0:
           n = n//2
       else:
           n = 3*n+1
       print(n)
    print(str(it)+" steps")

collatz(4)
collatz(10)

## 2
## 1
## 2 steps
## 5
## 16
## 8
## 4
## 2
## 1
## 6 steps

Some questions to think about:

• when is the sequence of minimal length?
• how does the length grow with the size of the initial \(n\)?

But be careful!