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 A287566 #6 Jul 20 2023 17:56:33
%S A287566 0,2,3,1,3,1,0,2,1,0,2,3,2,3,1,0,1,0,2,3,2,3,1,0,0,2,3,1,3,1,0,2,2,3,
%T A287566 1,0,0,2,3,1,3,1,0,2,1,0,2,3,3,1,0,2,1,0,2,3,2,3,1,0,0,2,3,1,2,3,1,0,
%U A287566 0,2,3,1,3,1,0,2,1,0,2,3,3,1,0,2,1,0
%N A287566 Start with 0 and repeatedly substitute 0->0231, 1->2310, 2->3102, 3->1023.
%C A287566 This is the fixed point of the morphism 0->0231, 1->2310, 2->3102, 3->1023 starting with 0. Let t be the (nonperiodic) sequence of positions of 0, and likewise, u for 1, v for 2, and w for 3; then t(n)/n -> 4, u(n)/n -> 4, v(n)/n -> 4, w(n)/n -> 4. Also, t(n) + u(n) + v(n) + w(n) = 16*n - 6 for n >= 1. See A287556 for a guide to related sequences.
%H A287566 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F A287566 a(n) = 4n - A287568(n) for n >= 1.
%e A287566 First three iterations of the morphism:
%e A287566 0231
%e A287566 0231310210232310
%e A287566 0231310210232310102323100231310223100231310210233102102323100231
%t A287566 s = Nest[Flatten[# /. {0 -> {0, 2, 3, 1}, 1 -> {2, 3, 2, 0}, 2 -> {3, 1, 0, 2}, 3 -> {1, 0, 2, 3}}] &, {0}, 9]; (* A287566 *)
%t A287566 Flatten[Position[s, 0]]; (* A287567 *)
%t A287566 Flatten[Position[s, 1]]; (* A287568 *)
%t A287566 Flatten[Position[s, 2]]; (* A287569 *)
%t A287566 Flatten[Position[s, 3]]; (* A287570 *)
%t A287566 Flatten[SubstitutionSystem[{0->{0,2,3,1},1->{2,3,1,0},2->{3,1,0,2},3->{1,0,2,3}},{0},{4}]] (* _Harvey P. Dale_, Jul 20 2023 *)
%Y A287566 Cf. A287567, A287568, A287569, A287570.
%K A287566 nonn,easy
%O A287566 1,2
%A A287566 _Clark Kimberling_, May 31 2017