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 A287320 #12 Jun 17 2025 00:37:53
%S A287320 0,0,2,2,1,0,0,0,2,2,1,0,2,2,1,0,2,2,1,0,1,0,1,0,0,0,2,2,1,0,0,0,2,2,
%T A287320 1,0,0,0,2,2,1,0,2,2,1,0,2,2,1,0,1,0,1,0,0,0,2,2,1,0,2,2,1,0,2,2,1,0,
%U A287320 1,0,1,0,0,0,2,2,1,0,2,2,1,0,2,2,1,0
%N A287320 0-limiting word of the morphism 0->10, 1->22, 2->0.
%C A287320 Starting with 0, the first 5 iterations of the morphism yield words shown here:
%C A287320 1st: 10
%C A287320 2nd: 2210
%C A287320 3rd: 002210
%C A287320 4th: 1010002210
%C A287320 5th: 221022101010002210
%C A287320 The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 mod 3.
%C A287320 Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where
%C A287320 U = 2.28537528186132044169516884721360670506...,
%C A287320 V = 3.87512979416277882597397059430967806752...,
%C A287320 W = 3.28537528186132044169516884721360670506...
%C A287320 If n >= 2, then u(n) - u(n-1) is in {1,2,4}, v(n) - v(n-1) is in {2,4,6}, and w(n) - w(n-1) is in {1,3,5,9}.
%H A287320 Clark Kimberling, <a href="/A287320/b287320.txt">Table of n, a(n) for n = 1..10000</a>
%e A287320 3rd iterate: 002210
%e A287320 6th iterate: 002210002210221022101010002210
%t A287320 s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 2}, 2 -> 0}] &, {0}, 12] (* A287320 *)
%t A287320 Flatten[Position[s, 0]] (* A287321 *)
%t A287320 Flatten[Position[s, 1]] (* A287322 *)
%t A287320 Flatten[Position[s, 2]] (* A287323 *)
%t A287320 SubstitutionSystem[{0->{1,0},1->{2,2},2->{0}},{2},{10}][[1]] (* _Harvey P. Dale_, Aug 17 2022 *)
%Y A287320 Cf. A287321, A287322, A287323, A287181. A298200.
%K A287320 nonn,easy
%O A287320 1,3
%A A287320 _Clark Kimberling_, May 23 2017