A Hailstone Number is a number relating to a sequence of integers that go up and down like a Hailstone in a cloud before it eventually falls to the ground. A hailstone number will eventually reach 1 before becoming stuck the short sequence of 4,2, 1.
One possible hailstone method is:
It can be described using Pseudo Code in the following way:
READ number (positive integer)
SET steps = 0
WHILE number != 1
IF number is odd THEN
number = (number * 3) + 1
number = number / 2
steps = steps + 1
Write a program to perform these calculations and find answers to the following questions:
Do all numbers reach 1? In other words, are all numbers hailstone numbers?
Can you find any numbers that take a long time to reach 1? (say a thousand steps?)
What happens if you change the rules? You may find another interesting property of numbers.