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 A367620 #26 Jan 09 2025 12:36:28 %S A367620 20,22,46,107,178,260,262,284,327,401,415,469,564,610,616,682,709,807, %T A367620 885,944,993,1024,1065,1116,1177,1248,1329,1420,1421,1432,1453,1484, %U A367620 1525,1576,1637,1708,1789,1880,1881,1892,1913,1944,1985,2037,2109,2201,2213,2245,2297,2369,2461,2473,2505,2557,2629,2721,2733,2765 %N A367620 The lexicographically earliest infinite sequence of positive numbers in which each term is a comma-child of the previous term. %C A367620 Discovered by _David W. Wilson_ in 2007 (see 2016 Angelini link). %C A367620 The first choice point occurs for the term after a(412987860) = 19999999918, which has two comma-children. %C A367620 We do not know which choice to take at that point. We do know by König's Infinity Lemma that one or both forks will extend to infinity. The definition of this sequence requires that we choose the smallest fork that has an infinite continuation. %C A367620 Update, Dec 22 2023: We now know that the start of this sequence is one of four candidates (all other possible starts having terminated). The shortest of the four possible starts has length %C A367620 8278670191169895553395510925614764265575448369172463113087634743486440833078554 %C A367620 In other words, we know that there are only four possibilities for the initial prefix of that length. %H A367620 N. J. A. Sloane, <a href="/A367620/b367620.txt">Table of n, a(n) for n = 1..20000</a> %H A367620 Eric Angelini, <a href="/A121805/a121805.pdf">The Commas Sequence</a>, Message to Sequence Fans, Sep 06 2016. [Cached copy, with permission] %H A367620 Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, <a href="http://arxiv.org/abs/2401.14346">arXiv:2401.14346</a>, Fibonacci Quarterly 62:3 (2024), 215-232. %H A367620 Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, <a href="/A121805/a121805_1.pdf">The Comma Sequence: A Simple Sequence With Bizarre Properties</a>, Local copy. %H A367620 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=_EHAdf6izPI">Eric Angelini's Comma Sequence</a>, Experimental Math Seminar, Rutgers Univ., January 18, 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane2024.pdf">Slides</a> %Y A367620 Cf. A121805, A367338, A367346. %K A367620 nonn,base %O A367620 1,1 %A A367620 _Michael S. Branicky_ and _N. J. A. Sloane_, Dec 20 2023