Problem 5: Hailstone (100pts)

Douglas Hofstadter's Pulitzer-prize-winning book, Gödel, Escher, Bach, poses the following mathematical puzzle.

1. Pick a positive integer \( x \) as the start.
2. If \( x \) is even, divide it by 2.
3. If \( x \) is odd, multiply it by 3 and add 1.
4. Continue this process until \( x \) is 1.

The number \( x \) will travel up and down but eventually end at 1 (at least for all numbers that have ever been tried -- nobody has ever proved that the sequence will terminate). Analogously, a hailstone travels up and down in the atmosphere before eventually landing on earth.

Breaking News (or at least the closest thing to that in math). There has been a recent development in the hailstone conjecture that shows that almost all numbers will eventually get to 1 if you repeat this process. This isn't a complete proof but a major breakthrough.

This sequence of values of \( x \) is often called a Hailstone sequence. Write a function that takes a single argument with formal parameter name \( x \), prints out the hailstone sequence starting at \( x \), and returns the number of steps in the sequence:

def hailstone(x):
    """Print the hailstone sequence starting at x and return its
    length.

    >>> a = hailstone(10)
    10
    5
    16
    8
    4
    2
    1
    >>> a
    7
    """
    "*** YOUR CODE HERE ***"

Hailstone sequences can get quite long! Try 27. What's the longest you can find?