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