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 A287520 #14 Oct 02 2019 21:23:59 %S A287520 0,1,2,1,0,2,1,2,0,1,0,2,0,1,2,1,2,0,1,0,2,1,2,0,0,1,2,1,0,2,0,1,2,1, %T A287520 2,0,0,1,2,1,0,2,1,2,0,1,0,2,1,2,0,0,1,2,1,0,2,0,1,2,1,2,0,1,0,2,1,2, %U A287520 0,0,1,2,0,1,2,1,0,2,1,2,0,1,0,2,0,1 %N A287520 Start with 0 and repeatedly substitute 0->012, 1->102, 2->120. %C A287520 This is the fixed point of the morphism 0->012, 1->102, 2->120 starting with 0. Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3, w(n)/n -> 3. %C A287520 It is in fact easy to see that |u(n)-3n|<3, |v(n)-3n|<3, and |w(n)-3n|<3. - _Michel Dekking_, Oct 02 2019 %C A287520 See A287385 for a guide to related sequences. %H A287520 Clark Kimberling, <a href="/A287520/b287520.txt">Table of n, a(n) for n = 1..10000</a> %H A287520 <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a> %e A287520 First three iterations of the morphism: 012, 012102120, 012102120102012120102120012. %t A287520 s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287520*) %t A287520 Flatten[Position[s, 0]]; (* A287521 *) %t A287520 Flatten[Position[s, 1]]; (* A287522 *) %t A287520 Flatten[Position[s, 2]]; (* A189630, conjectured *) %Y A287520 Cf. A287385, A287521, A287522, A189630. %K A287520 nonn,easy %O A287520 1,3 %A A287520 _Clark Kimberling_, May 30 2017