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A286998 0-limiting word of the morphism 0->10, 1->20, 2->0. 6

%I

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

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

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

%N 0-limiting word of the morphism 0->10, 1->20, 2->0.

%C Starting with 0, the first 5 iterations of the morphism yield words shown here:

%C 1st: 10

%C 2nd: 2010

%C 3rd: 0102010

%C 4th: 1020100102010

%C 5th: 201001020101020100102010

%C The 2-limiting word is the limit of the words for which the number of iterations is congruent to 2 mod 3.

%C Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where

%C U = 1.8392867552141611325518525646532866...,

%C V = U^2 = 3.3829757679062374941227085364...,

%C W = U^3 = 6.2222625231203986266745611011....

%C If n >=2, then u(n) - u(n-1) is in {1,2}, v(n) - v(n-1) is in {2,3,4}, and w(n) - w(n-1) is in {4,6,7}.

%H Clark Kimberling, <a href="/A286998/b286998.txt">Table of n, a(n) for n = 1..10000</a>

%e 3rd iterate: 0102010

%e 6th iterate: 01020101020100102010201001020101020100102010

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 0}, 2 -> 0}] &, {0}, 9] (* A286998 *)

%t Flatten[Position[s, 0]] (* A286999 *)

%t Flatten[Position[s, 1]] (* A287000 *)

%t Flatten[Position[s, 2]] (* A287001 *)

%Y Cf. A286999, A287000, A287001, A287112, A287174.

%K nonn,easy

%O 1,4

%A _Clark Kimberling_, May 22 2017

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Last modified June 19 13:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)