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A287397 Start with 0 and repeatedly substitute 0->012, 1->210, 2->102. 5

%I

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

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

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

%N Start with 0 and repeatedly substitute 0->012, 1->210, 2->102.

%C This is the fixed point of the morphism 0->012, 1->210, 2->102 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="/A287397/b287397.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, 012210021, 012210021021210012012021210.

%t s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 1, 0}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287397*)

%t Flatten[Position[s, 0]]; (*A287398*)

%t Flatten[Position[s, 1]]; (*A287399*)

%t Flatten[Position[s, 2]]; (*A287400*)

%Y Cf. A287385. A287398, A287399, A287400.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, May 25 2017

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)