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Open Problems in Communication and Computation pp 4–26Cite as

FRACTRAN: A Simple Universal Programming Language for Arithmetic

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Abstract

To play the fraction game corresponding to a given list

$${{f}_{1}},{{f}_{2}}, \ldots ,{{f}_{k}}$$

of fractions and starting integer N, you repeatedly multiply the integer you have at any stage (initially N) by the earliest f i in the list for which the answer is integral. Whenever there is no such f i, the game stops.

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References

  1. J.H. Conway, “Unpredictable Iterations,” in Proceedings of the Number Theory Conference, Boulder, Colorado, pp. 49–52 (1972).

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  2. J.H. Conway, “FRACTRAN - A Simple Universal Programming Language for Arithmetic,” Open Problems Commun. Comput., pp. 4–26 (1986).

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  3. J.C. Lagarias, “The 3x + 1 Problem and Its Generalizations,” Am. Math. Monthly, 92, No. 1, pp. 3–25 (1985).

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  4. K. Mahler, “On the Approximation of π,” Indagnationes Math., 15, pp. 30–42 (1953).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    J. H. Conway

Authors
  1. J. H. Conway
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Editor information

Editors and Affiliations

  1. Departments of Electrical Engineering and Statistics, Stanford University, Stanford, California, USA

    Thomas M. Cover

  2. Systems Principles Research, Bell Communications Research, Morristown, New Jersey, USA

    B. Gopinath

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© 1987 Springer-Verlag New York Inc.

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Conway, J.H. (1987). FRACTRAN: A Simple Universal Programming Language for Arithmetic. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_2

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  • DOI: https://doi.org/10.1007/978-1-4612-4808-8_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9162-6

  • Online ISBN: 978-1-4612-4808-8

  • eBook Packages: Springer Book Archive

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