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%I #15 Jan 22 2023 16:03:15
%S 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 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 6,3,5,5,9,7,7,7,6,4,6,7,5,5,8,5,6,6,4
%N 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 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 This sequence is unbounded (this is a consequence of Van der Waerden's theorem).
%H Rémy Sigrist, <a href="/A350226/b350226.txt">Table of n, a(n) for n = 0..8191</a>
%H Rémy Sigrist, <a href="/A350226/a350226.txt">C program for A350226</a>
%e For n = 12:
%e - the first 13 terms of A010060 are:
%e 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0
%e ^ ^ ^ ^ ^
%e - A010060(0) = A010060(3) = A010060(6) = A010060(9) = A010060(12),
%e - and there is no longer sequence of distinct numbers <= 12 in arithmetic progression ending in 12 with this property,
%e - so a(12) = 5.
%o (C) See Links section.
%Y Cf. A005346, A010060, A342818, A342827, A350235 (records), A350285 (least first differences).
%K nonn
%O 0,3
%A _Rémy Sigrist_, Dec 20 2021
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