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FRACTRAN: A Simple Universal Programming Language for Arithmetic

  • J. H. Conway

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.

Keywords

Computable Function FRACTRAN Program Universal Program Partial Recursive Function Normal Form Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    J.H. Conway, “Unpredictable Iterations,” in Proceedings of the Number Theory Conference, Boulder, Colorado, pp. 49–52 (1972).Google Scholar
  2. [2]
    J.H. Conway, “FRACTRAN - A Simple Universal Programming Language for Arithmetic,” Open Problems Commun. Comput., pp. 4–26 (1986).Google Scholar
  3. [3]
    J.C. Lagarias, “The 3x + 1 Problem and Its Generalizations,” Am. Math. Monthly, 92, No. 1, pp. 3–25 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    K. Mahler, “On the Approximation of π,” Indagnationes Math., 15, pp. 30–42 (1953).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • J. H. Conway
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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