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 A287561 #4 May 31 2017 16:14:54
%S A287561 0,2,1,3,1,3,0,2,2,1,3,0,3,0,2,1,2,1,3,0,3,0,2,1,0,2,1,3,1,3,0,2,1,3,
%T A287561 0,2,2,1,3,0,3,0,2,1,0,2,1,3,3,0,2,1,0,2,1,3,1,3,0,2,2,1,3,0,1,3,0,2,
%U A287561 2,1,3,0,3,0,2,1,0,2,1,3,3,0,2,1,0,2
%N A287561 Start with 0 and repeatedly substitute 0->0213, 1->2130, 2->1302, 3->3021.
%C A287561 This is the fixed point of the morphism 0->0213, 1->2130, 2->1302, 3->3021 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 A287561 Clark Kimberling, <a href="/A287561/b287561.txt">Table of n, a(n) for n = 1..20000</a>
%H A287561 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%F A287561 a(n) = 4n - A287565(n) for n >= 1.
%e A287561 First three iterations of the morphism:
%e A287561 0213
%e A287561 0213130221303021
%e A287561 0213130221303021213030210213130213022130302102133021021313022130
%t A287561 s = Nest[Flatten[# /. {0 -> {0, 2, 1, 3}, 1 -> {2, 1, 3, 0}, 2 -> {1, 3, 0, 2}, 3 -> {3, 0, 2, 1}}] &, {0}, 9]; (* A287561 *)
%t A287561 Flatten[Position[s, 0]]; (* A287562 *)
%t A287561 Flatten[Position[s, 1]]; (* A287563 *)
%t A287561 Flatten[Position[s, 2]]; (* A287564 *)
%t A287561 Flatten[Position[s, 3]]; (* A287565 *)
%Y A287561 Cf. A287562, A287563, A287564, A287565.
%K A287561 nonn,easy
%O A287561 1,2
%A A287561 _Clark Kimberling_, May 31 2017