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1-limiting word of the morphism 0->10, 1->0010.
10

%I #16 May 19 2021 05:24:49

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

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

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

%N 1-limiting word of the morphism 0->10, 1->0010.

%C The morphism 0->10, 1->0010 has two limiting words. If the number of iterations is even, the 0-word evolves from 0 -> 10 -> 001010 -> 1010001010001010 -> 00101000101010100010100010101010001010001010, as in A285139; if the number of iterations is odd, the 1-word evolves from 0 -> 10 -> 001010 -> 1010001010001010 (here).

%H Clark Kimberling, <a href="/A285142/b285142.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 0, 1, 0}}] &, {0}, 11]; (* A285142 *)

%t Flatten[Position[s, 0]]; (* A285143 *)

%t Flatten[Position[s, 1]]; (* A285144 *)

%Y Cf. A285139, A285143, A285144.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 20 2017

%E Definition and comment corrected by _Georg Fischer_, May 14 2021