A350556 -id:A350556 - cp's OEIS frontend

A350555 Numerators of Conway's PIGAME.

365, 29, 79, 679, 3159, 83, 473, 638, 434, 89, 17, 79, 31, 41, 517, 111, 305, 23, 73, 61, 37, 19, 89, 41, 833, 53, 86, 13, 23, 67, 71, 83, 475, 59, 41, 1, 1, 1, 1, 89

Offset: 1

Paolo Xausa, Jan 05 2022

These rational numbers represent a FRACTRAN program that generates the decimal expansion of Pi (A000796).
Conway proves that, when this program is started at 2^k (with k >= 0), the next power of 2 to appear is 2^Pi_d(k), where Pi_d(0) = 3 and, for k >= 1, Pi_d(k) is the k-th digit after the point in the decimal expansion of Pi.
According to Kaushik, Murphy, and Weed, the starting value should be 89*2^k. - Andrei Zabolotskii, Aug 23 2025

J. H. Conway, "FRACTRAN: A Simple Universal Programming Language for Arithmetic", in J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, p. 249, and in T. M. Cover and B. Gopinath, eds, Open Problems in Communication and Computation, Springer, New York, NY, 1987, pp. 4-26.
Khushi Kaushik, Tommy Murphy, and David Weed, Computing sqrt(2) with FRACTRAN, Irish Math. Soc. Bull., 95 (2025), 23-34 (warning: theorem 3.1 is missing the last fraction 1/97); arXiv:2412.16185 [cs.PL], 2024.
Wikipedia, FRACTRAN.

Cf. A000796, A202138, A350556 (denominators).

A350664 Denominators of Conway's POLYGAME.

Original entry on oeis.org

559, 551, 527, 517, 329, 129, 115, 86, 53, 47, 46, 43, 41, 37, 31, 31, 29, 23, 15, 19, 7, 17, 13, 3

Offset: 1

Paolo Xausa, Jan 10 2022

See A350663 for numerators, comments and links.

Cf. A203363, A350556, A350663.

cp's OEIS Frontend

A350555 Numerators of Conway's PIGAME.

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