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 A079730 #22 Jul 25 2023 10:12:53
%S A079730 1,2,2,3,3,4,4,4,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,1,2,3,4,4,1,1,2,2,3,3,
%T A079730 4,4,4,1,1,1,2,2,2,3,3,3,4,4,4,4,1,1,1,1,2,2,2,2,3,3,3,3,4,1,1,2,2,2,
%U A079730 3,3,3,3,4,4,4,4,1,2,3,3,4,4,1,1,1,2,2,2,3,3,3,3,4,4,4,4,1,1,1,1,2,3,4,1,1
%N A079730 Kolakoski variation using (1,2,3,4) starting with 1,2.
%C A079730 a(1)=1 then a(n) is the length of n-th run. This kind of Kolakoski variation using(1,2,3,4,...,m) as m grows reaches the Golomb's sequence A001462.
%H A079730 Ivan Neretin, <a href="/A079730/b079730.txt">Table of n, a(n) for n = 1..10000</a>
%H A079730 Ulrich Reitebuch, Henriette-Sophie Lipschütz, and Konrad Polthier, <a href="https://archive.bridgesmathart.org/2023/bridges2023-481.html">Visualizing the Kolakoski Sequence</a>, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 481-484.
%F A079730 Partial sum sequence is expected to be asymptotic to 5/2*n.
%e A079730 Sequence begins: 1,2,2,3,3,4,4,4,1,1,1,2,2,2,2,3,3,3,3, read it as: (1),(2,2),(3,3),(4,4,4),(1,1,1),(2,2,2,2),(3,3,3,3),... then count the terms in parentheses to get: 1,2,2,3,3,4,4,.. which is the same sequence.
%t A079730 seed = {1, 2, 3, 4};
%t A079730 w = {};
%t A079730 i = 1;
%t A079730 Do[
%t A079730 w = Join[w,
%t A079730 Array[seed[[Mod[i - 1, Length[seed]] + 1]] &,
%t A079730 If[i > Length[w], seed, w][[i]]]];
%t A079730 i++
%t A079730 , {n, 41}];
%t A079730 w
%Y A079730 Cf. A000002.
%K A079730 nonn
%O A079730 1,2
%A A079730 _Benoit Cloitre_, Feb 17 2003
%E A079730 Corrected by _Ivan Neretin_, Apr 01 2015