The Hailstone Series

Introduction

The January 1984 issue of Scientific American contains an article describing an interesting sequence of numbers known as the Hailstone Series. The series is formed like this:

1. Pick a positive integer.
2. If it's odd, triple the number and add one.
3. If it's even, divide the number by two.
4. Go back to 2.

Although the numbers usually bob up and down, they eventually they reach a repeating "ground" state: 4 2 1 4 2 1 ... This has been proven for every number up to about 1.2E12

Example

For example, here is the sequence generated for an initial value of 26:

• 26 - even, so divide it by 2...
• 13 - odd, triple it (getting 39), and add 1...
• 40 - even, divide by 2...
• 20 - again
• 10 - etc., etc.
• 5
• 16
• 8
• 4
• 2
• 1
• 4
• ...

Make sure you undertand how each successive number was obtained, using the rules listed at the top.

Problem Statement

You will write a program to generate the Hailstone Series for initial values entered by the user. Your program should answer the following questions after the ground state has been reached:

1. How many items are in the sequence?
2. What is the largest number the sequence reaches along the way?

For the first question you should stop counting once any member of the sequence 4 2 1 is reached. If a member of the ground state is entered as the initial value, then the length of the sequence is just 1.

For example, if 8 is entered as the initial value, then the answer to question #1 is 2 (i.e., it stopped counting when 4 was encountered).

Go back and look at the sequence you made with the starting value of 26, and answer the two questions. You should find that there are 9 items in the list, with 40 being the maximum.

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Goal Analysis and A Staged Solution

(this section has been removed for now because students are doing this assignment - please email me if you want the original file)