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A287356 Start with 0 and repeatedly substitute 0->11, 1->12, 2->0. 4

%I #5 May 24 2017 20:55:38

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

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

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

%N Start with 0 and repeatedly substitute 0->11, 1->12, 2->0.

%C This is the fixed point of the morphism 0->11, 1->12, 2->0 starting with 0. Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. 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 = 5.5707505637226408833903376944272134...,

%C V = 1.9375648970813894129869852971548390...,

%C W = 3.2853752818613204416951688472136067....

%H Clark Kimberling, <a href="/A287356/b287356.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>

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 2}, 2 -> 0}] &, {0}, 11] (* A287356 *)

%t Flatten[Position[s, 0]] (* A287357 *)

%t Flatten[Position[s, 1]] (* A287358 *)

%t Flatten[Position[s, 2]] (* A287359 *)

%Y Cf. A287357, A287358, A287359.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 24 2017

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Last modified March 3 06:28 EST 2024. Contains 370499 sequences. (Running on oeis4.)