- Take the natural number $n$.
- If $n$ is even: divide it by 2 to get $\frac{n}{2}$.
- If $n$ is odd: multiply it by 3 and add 1 to obtain $3n+1$.

- Repeat the process indefinitely

For every natural number $n$, the “Half Or Triple Plus One” algorithm will eventually lead to the number 1, at which point it will loop forever:

1 → 4 → 2 → 1

This implies two things:

- The algorithm always eventually decreases
- There are not cycles besides the
`1 → 4 → 2 → 1`cycle

- Understand this program which prints the “collatz sequence” for 27.

n = 27 while n > 1: print n if n % 2 == 0: n /= 2 else: n = n*3 + 1

Note

The expression `if x % 2 == 0:` *means* the same thing as `if x is even:`.

- Modify the program so that it prints the collatz sequences for every number from 1 to 100.
- Modify your program so that it prints the number between 2 and 1000 with the longest collatz sequence.