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 A352746 #8 Apr 07 2022 00:36:07 %S A352746 0,1,1,1,2,2,3,4,3,3,4,5,4,5,4,4,5,4,5,6,5,6,5,5,6,7,6,5,6,5,6,7,6,5, %T A352746 6,7,6,7,6,6,7,8,7,6,7,6,7,8,7,8,7,7,8,6,7,8,7,6,7,8,7,8,7,7,8,6,7,8, %U A352746 7,8,7,7,8,9,8,7,8,7,8,9,8,9,8,8,9,7,8 %N A352746 a(n) is the number of Lyndon factors of the Thue-Morse string of length n. %C A352746 The Thue-Morse string of length n is the length-n prefix of the infinite Thue-Morse string. The sequence starts: "", "0", "01", "011", "0110", "01101", "011010", ... %H A352746 Augustin Ido and Guy Melançon, <a href="http://dml.mathdoc.fr/item/01375570/">Lyndon factorization of the Thue-Morse word and its relatives</a>, Discret. Math. Theor. Comput. Sci. 1997. %H A352746 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lyndon_word">Lyndon word</a> %e A352746 The Lyndon factorization of the Thue-Morse strings of length n = 0..9. %e A352746 [0] [] %e A352746 [1] ["0"] %e A352746 [2] ["01"] %e A352746 [3] ["011"] %e A352746 [4] ["011", "0"] %e A352746 [5] ["011", "01"] %e A352746 [6] ["011", "01", "0"] %e A352746 [7] ["011", "01", "0", "0"] %e A352746 [8] ["011", "01", "001"] %e A352746 [9] ["011", "01", "0011"] %p A352746 with(StringTools): A352746 := n -> nops(LyndonFactors(ThueMorse(n))): %p A352746 seq(A352746(n), n = 0..12); %Y A352746 Cf. A000045, A014707, A074650, A211100, A352745. %K A352746 nonn %O A352746 0,5 %A A352746 _Peter Luschny_, Apr 06 2022