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A285083 1-limiting word of the morphism 0->10, 1-> 011. 6

%I

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

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

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

%N 1-limiting word of the morphism 0->10, 1-> 011.

%C The morphism 0->10, 1->011 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 01110 -> 1001101101110 -> 0111010011011100110111001101101110, as in A285080; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 01110 -> 1001101101110, as in A285083.

%C Let v(n) = position of n-th 1. Then v(n)/n -> (1+sqrt(5))/2, the golden ratio (A001622); see A285082.

%H Clark Kimberling, <a href="/A285083/b285083.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 1, 1}}] &, {0}, 13]; (* A285083 *)

%t Flatten[Position[s, 0]]; (* A285084 *)

%t Flatten[Position[s, 1]]; (* A285085 *)

%Y Cf. A001622, A285080, A285084, A285085.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 19 2017

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)