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 A211098 #12 Mar 30 2023 09:16:24 %S A211098 1,1,1,2,1,1,1,3,2,3,1,1,1,1,1,4,3,4,2,2,3,4,1,1,1,1,1,1,1,1,1,5,4,5, %T A211098 3,5,4,5,2,2,2,5,3,3,4,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6,5,6,4,6, %U A211098 5,6,3,3,5,6,4,6,5,6,2,2,2,2,2,2,5,6,3,3,3,3,4,4,5,6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A211098 Length of largest (i.e., leftmost) Lyndon word in Lyndon factorization of binary vectors of lengths 1, 2, 3, ... %C A211098 Any binary word has a unique factorization as a product of nonincreasing Lyndon words (see Lothaire). Here we look at the Lyndon factorizations of the binary vectors 0,1, 00,01,10,11, 000,001,010,011,100,101,110,111, 0000,... %C A211098 See A211097, A211099, A211100 for further information, including Maple code. %C A211098 The smallest (or rightmost) factors are given by A211095 and A211096, offset by 2. %D A211098 M. Lothaire, Combinatorics on Words, Addison-Wesley, Reading, MA, 1983. See Theorem 5.1.5, p. 67. %D A211098 G. Melançon, Factorizing infinite words using Maple, MapleTech Journal, vol. 4, no. 1, 1997, pp. 34-42 %H A211098 N. J. A. Sloane, <a href="/A211097/a211097.txt">Maple programs for A211097 etc.</a> %e A211098 Here are the Lyndon factorizations of the first few binary vectors: %e A211098 .0. %e A211098 .1. %e A211098 .0.0. %e A211098 .01. %e A211098 .1.0. %e A211098 .1.1. %e A211098 .0.0.0. %e A211098 .001. %e A211098 .01.0. %e A211098 .011. %e A211098 .1.0.0. %e A211098 .1.01. %e A211098 .1.1.0. %e A211098 .1.1.1. %e A211098 .0.0.0.0. %e A211098 ... %Y A211098 Cf. A001037 (number of Lyndon words of length m); A102659 (list thereof), A211100. %Y A211098 Cf. A211095-A211099. %K A211098 nonn %O A211098 1,4 %A A211098 _N. J. A. Sloane_, Apr 01 2012