Sequences of Integers generated in the Collatz Problem. 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 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, ....

**References**

Schwartzman, S. *The Words of Mathematics: An Etymological Dictionary of
Mathematical Terms Used in English.* Washington, DC: Math. Assoc. Amer., 1994.

© 1996-9

1999-05-25