TOPICS

# Hailstone Number

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 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, ....

Collatz Problem

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## References

Pickover, C. A. "Hailstone Numbers." Ch. 49 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Oxford, England: Oxford University Press, pp. 116-118, 2001.Schwartzman, S. The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. Washington, DC: Math. Assoc. Amer., 1994.

Hailstone Number

## Cite this as:

Weisstein, Eric W. "Hailstone Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HailstoneNumber.html