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 A338623 #19 Jul 19 2021 01:22:52 %S A338623 0,0,1,1,2,2,2,2,3,4,4,4,4,4,4,4,5,6,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,10, %T A338623 11,12,13,14,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16, %U A338623 16,16,16,16,16,16,16,17,18,19,20,21,22,23,24,25 %N A338623 a(n) is the length of the longest block of consecutive terms appearing twice (possibly with overlap) among the first n terms of the Thue-Morse sequence (A010060). %C A338623 This sequence is weakly increasing and unbounded (as A010060 is bounded). %H A338623 Rémy Sigrist, <a href="/A338623/b338623.txt">Table of n, a(n) for n = 1..8192</a> %H A338623 Rémy Sigrist, <a href="/A338623/a338623.gp.txt">PARI program for A338623</a> %F A338623 a(n) <= a(n+1) <= a(n) + 1. %F A338623 a(A304588(n)) = n (and this is the first occurrence of n in the sequence). %e A338623 For n = 8: %e A338623 - the first 8 terms of A010060 are 0, 1, 1, 0, 1, 0, 0, 1, %e A338623 - the blocks (0, 1) and (1, 0) are repeated, and there are no length-3 repeated block, %e A338623 - so a(8) = 2. %o A338623 (PARI) See Links section. %Y A338623 Cf. A010060, A304588, A338624 (Kolakoski variant). %K A338623 nonn %O A338623 1,5 %A A338623 _Rémy Sigrist_, Nov 04 2020