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 A105258 #11 Oct 02 2016 10:13:15
%S A105258 1,1,2,1,2,2,1,3,1,2,2,1,3,2,1,3,1,3,2,1,1,2,2,1,3,2,1,3,1,3,2,1,2,1,
%T A105258 3,1,3,2,1,1,3,2,1,2,1,1,3,2,1,2,2,1,3,2,1,3,1,3,2,1,2,1,3,1,3,2,1,1,
%U A105258 3,2,1,2,1,1,3,2,2,1,3,1,3,2,1,1,3,2,1,2,1,1,3,2,1,3,2,1,2,1,1,3,2,2,1,1,3
%N A105258 Triangle of trajectory of 1 under the morphism 1->2, 2->13, 3->1.
%H A105258 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e A105258 The first steps are:
%e A105258 {1}
%e A105258 {1, 2}
%e A105258 {1, 2, 2, 1, 3}
%e A105258 {1, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1}
%t A105258 s[1] = {2}; s[2] = {1, 3}; s[3] = {1}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 6}]]
%o A105258 (PARI) {a(n)=local(m, v, w); v=w=[1]; while(length(w)<n, m=length(v); for(k=1, m, v=concat(v, [[2],[1,3],[1]][v[k]])); w=concat(w, v)); w[n]}
%Y A105258 Cf. A073058, A105111.
%K A105258 nonn,tabf
%O A105258 0,3
%A A105258 _Roger L. Bagula_, Apr 14 2005
%E A105258 Edited by the Associate Editors of the OEIS, Apr 07 2009