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

1,1

Comments

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

Links

Table of n, a(n) for n=1..40.

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.

Crossrefs

Cf. A000796, A202138, A350556 (denominators).

Sequence in context: A098252 A221393 A099113 * A073304 A011763 A116354

Adjacent sequences: A350552 A350553 A350554 * A350556 A350557 A350558

Keyword

nonn,frac,fini,full

Author

Paolo Xausa, Jan 05 2022

Status

approved