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