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 A211099 #13 Mar 30 2023 07:09:24 %S A211099 1,2,1,12,2,2,1,112,12,122,2,2,2,2,1,1112,112,1122,12,12,122,1222,2,2, %T A211099 2,2,2,2,2,2,1,11112,1112,11122,112,11212,1122,11222,12,12,12,12122, %U A211099 122,122,1222,12222,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,111112,11112,111122,1112,111212,11122,111222,112,112,11212,112122,1122,112212,11222,112222,12 %N A211099 Largest (i.e., leftmost) Lyndon word in Lyndon factorization of binary vectors of lengths 1, 2, 3, ... (written using 1's and 2's rather than 0's and 1's, since numbers > 0 in the OEIS cannot begin with 0). %C A211099 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 A211099 See A211097, A211099, A211100 for further information, including Maple code. %C A211099 The smallest (or rightmost) factors are given by A211095 and A211096, offset by 2. %D A211099 M. Lothaire, Combinatorics on Words, Addison-Wesley, Reading, MA, 1983. See Theorem 5.1.5, p. 67. %D A211099 G. Melançon, Factorizing infinite words using Maple, MapleTech Journal, vol. 4, no. 1, 1997, pp. 34-42 %H A211099 N. J. A. Sloane, <a href="/A211097/a211097.txt">Maple programs for A211097 etc.</a> %e A211099 Here are the Lyndon factorizations of the first few binary vectors: %e A211099 .0. %e A211099 .1. %e A211099 .0.0. %e A211099 .01. %e A211099 .1.0. %e A211099 .1.1. %e A211099 .0.0.0. %e A211099 .001. %e A211099 .01.0. %e A211099 .011. %e A211099 .1.0.0. %e A211099 .1.01. %e A211099 .1.1.0. %e A211099 .1.1.1. %e A211099 .0.0.0.0. %e A211099 ... %e A211099 The real sequence (written with 0's and 1's rather than 1's and 2's) is: %e A211099 0, 1, 0, 01, 1, 1, 0, 001, 01, 011, 1, 1, 1, 1, 0, 0001, 001, 0011, 01, 01, 011, 0111, 1, 1, 1, 1, 1, 1, 1, 1, 0, 00001, 0001, 00011, 001, 00101, 0011, 00111, 01, 01, 01, 01011, 011, 011, 0111, 01111, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 000001, 00001, ... %Y A211099 Cf. A001037 (number of Lyndon words of length m); A102659 (list thereof), A211100. %Y A211099 Cf. A211095-A211099. %K A211099 nonn %O A211099 1,2 %A A211099 _N. J. A. Sloane_, Apr 01 2012