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a(n) is the length of the longest block of consecutive terms appearing twice (possibly with overlap) among the first n terms of the Kolakoski sequence (A000002).
3

%I #12 Jul 19 2021 01:22:59

%S 0,0,1,1,1,2,2,2,3,4,4,4,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,9,10,

%T 10,10,10,10,10,10,11,12,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,

%U 14,14,14,14,14,14,14,14,14,14,14,14,15,16,17,18,18

%N a(n) is the length of the longest block of consecutive terms appearing twice (possibly with overlap) among the first n terms of the Kolakoski sequence (A000002).

%C This sequence is weakly increasing and unbounded (as A000002 is bounded).

%H Rémy Sigrist, <a href="/A338624/b338624.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A338624/a338624.gp.txt">PARI program for A338624</a>

%F a(n) <= a(n+1) <= a(n) + 1.

%o (PARI) See Links section.

%Y Cf. A000002, A338623 (Thue-Morse variant).

%K nonn

%O 1,6

%A _Rémy Sigrist_, Nov 04 2020