Hailstone numbers are the integers in sequences associated with the Collatz conjecture. For
example, for a starting number of 7, the sequence is
7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, .... Such
sequences are called hailstone sequences because the
values typically rise and fall, somewhat analogously to a hailstone inside a cloud.
While a hailstone eventually becomes so heavy that it falls to ground, every starting positive integer ever tested has produced a hailstone
sequence that eventually drops down to the number 1 and then "bounces"
into the small loop 4, 2, 1, ....
