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A287411 Start with 0 and repeatedly substitute 0->012, 1->120, 2->021. 5

%I

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

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

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

%N Start with 0 and repeatedly substitute 0->012, 1->120, 2->021.

%C This is the fixed point of the morphism 0->012, 1->120, 2->021 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="/A287411/b287411.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, 012120021, 012120021120021012012021120.

%t s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287411*)

%t Flatten[Position[s, 0]]; (*A287412*)

%t Flatten[Position[s, 1]]; (*A287413*)

%t Flatten[Position[s, 2]]; (*A287414*)

%Y Cf. A287385, A287412, A287413, A287414.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, May 25 2017

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Last modified April 5 16:53 EDT 2020. Contains 333245 sequences. (Running on oeis4.)