Collatz conjecture
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Unsolved problem in mathematics: Does the Collatz sequence eventually reach 1 for all positive integer values?
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence.
It is named after mathematician Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate.[1] It is also known as the 3n + 1 problem, the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem.[2][3] The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud),[4][5] or as wondrous numbers.[6]
References
- ↑ O'Connor, J.J.; Robertson, E.F. (2006). "Lothar Collatz". St Andrews University School of Mathematics and Statistics, Scotland. http://www-history.mcs.st-andrews.ac.uk/Biographies/Collatz.html.
- ↑ Maddux, Cleborne D.; Johnson, D. Lamont (1997). Logo: A Retrospective. New York: Haworth Press. p. 160. ISBN 0-7890-0374-0. "The problem is also known by several other names, including: Ulam's conjecture, the Hailstone problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, and the Collatz problem."
- ↑ According to Lagarias (1985), p. 4, the name "Syracuse problem" was proposed by Hasse in the 1950s, during a visit to Syracuse University.
- ↑ Pickover, Clifford A. (2001). Wonders of Numbers. Oxford: Oxford University Press. pp. 116–118. ISBN 0-19-513342-0. https://archive.org/details/wondersnumbersad00pick.
- ↑ "Hailstone Number". MathWorld. Wolfram Research. http://mathworld.wolfram.com/HailstoneNumber.html.
- ↑ Hofstadter, Douglas R. (1979). Gödel, Escher, Bach. New York: Basic Books. pp. 400–2. ISBN 0-465-02685-0.
