This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350555 #19 Aug 23 2025 09:28:31 %S A350555 365,29,79,679,3159,83,473,638,434,89,17,79,31,41,517,111,305,23,73, %T A350555 61,37,19,89,41,833,53,86,13,23,67,71,83,475,59,41,1,1,1,1,89 %N A350555 Numerators of Conway's PIGAME. %C A350555 These rational numbers represent a FRACTRAN program that generates the decimal expansion of Pi (A000796). %C A350555 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. %C A350555 According to Kaushik, Murphy, and Weed, the starting value should be 89*2^k. - _Andrei Zabolotskii_, Aug 23 2025 %H A350555 J. H. Conway, "FRACTRAN: A Simple Universal Programming Language for Arithmetic", in J. C. Lagarias, ed., <a href="https://bookstore.ams.org/mbk-78">The Ultimate Challenge: The 3x+1 Problem</a>, American Mathematical Society, 2010, p. 249, and in T. M. Cover and B. Gopinath, eds, <a href="https://doi.org/10.1007/978-1-4612-4808-8_2">Open Problems in Communication and Computation</a>, Springer, New York, NY, 1987, pp. 4-26. %H A350555 Khushi Kaushik, Tommy Murphy, and David Weed, <a href="https://doi.org/10.33232/BIMS.0095.23.34">Computing sqrt(2) with FRACTRAN</a>, Irish Math. Soc. Bull., 95 (2025), 23-34 (warning: theorem 3.1 is missing the last fraction 1/97); arXiv:<a href="https://arxiv.org/abs/2412.16185">2412.16185</a> [cs.PL], 2024. %H A350555 Wikipedia, <a href="https://en.wikipedia.org/wiki/FRACTRAN">FRACTRAN</a>. %Y A350555 Cf. A000796, A202138, A350556 (denominators). %K A350555 nonn,frac,fini,full,changed %O A350555 1,1 %A A350555 _Paolo Xausa_, Jan 05 2022