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 A350226 #15 Jan 22 2023 16:03:15 %S A350226 1,1,2,2,2,2,3,3,2,4,3,2,5,3,3,6,2,3,7,4,5,3,4,3,5,5,4,4,6,3,6,7,2,4, %T A350226 3,5,7,7,4,6,5,5,6,3,5,6,3,6,5,7,7,5,5,4,7,4,8,6,4,4,6,6,7,8,2,3,8,5, %U A350226 6,3,5,5,9,7,7,7,6,4,6,7,5,5,8,5,6,6,4 %N A350226 a(n) is the length of the longest sequence of distinct numbers in arithmetic progression in the interval 0..n, ending with n and where the Thue-Morse sequence (A010060) is constant. %C A350226 In other words, a(n) is the greatest k > 0 such that A010060(n) = A010060(n - i*d) for i = 0..k-1 and some d > 0 (see A350285 for the least such d). %C A350226 This sequence is unbounded (this is a consequence of Van der Waerden's theorem). %H A350226 Rémy Sigrist, <a href="/A350226/b350226.txt">Table of n, a(n) for n = 0..8191</a> %H A350226 Rémy Sigrist, <a href="/A350226/a350226.txt">C program for A350226</a> %e A350226 For n = 12: %e A350226 - the first 13 terms of A010060 are: %e A350226 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0 %e A350226 ^ ^ ^ ^ ^ %e A350226 - A010060(0) = A010060(3) = A010060(6) = A010060(9) = A010060(12), %e A350226 - and there is no longer sequence of distinct numbers <= 12 in arithmetic progression ending in 12 with this property, %e A350226 - so a(12) = 5. %o A350226 (C) See Links section. %Y A350226 Cf. A005346, A010060, A342818, A342827, A350235 (records), A350285 (least first differences). %K A350226 nonn %O A350226 0,3 %A A350226 _Rémy Sigrist_, Dec 20 2021