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Start with 0 and repeatedly substitute 0->012, 1->201, 2->210.
4

%I #10 Jun 01 2022 18:09:26

%S 0,1,2,2,0,1,2,1,0,2,1,0,0,1,2,2,0,1,2,1,0,2,0,1,0,1,2,2,1,0,2,0,1,0,

%T 1,2,0,1,2,2,0,1,2,1,0,2,1,0,0,1,2,2,0,1,2,1,0,2,0,1,0,1,2,2,1,0,0,1,

%U 2,2,0,1,0,1,2,2,0,1,2,1,0,2,1,0,2,0

%N Start with 0 and repeatedly substitute 0->012, 1->201, 2->210.

%C This is the fixed point of the morphism 0->012, 1->201, 2->210 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 See A287385 for a guide to related sequences.

%H Clark Kimberling, <a href="/A287455/b287455.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, 012201210, 012201210210012201210201012.

%t s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{2, 1, 0}}] &, {0}, 9]; (*A287455*)

%t Flatten[Position[s, 0]]; (*A287456*)

%t Flatten[Position[s, 1]]; (*A287457*)

%t Flatten[Position[s, 2]]; (*A287458*)

%Y Cf. A287385, A287456, A287457, A287458.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, May 30 2017