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{0->100, 1->001}-transform of the infinite Fibonacci word A003849.
3

%I #5 Jun 04 2017 18:18:41

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

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

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

%N {0->100, 1->001}-transform of the infinite Fibonacci word A003849.

%C As a word, A003849 = 0100101001001010010100100..., and replacing each 0 by 100 and each 1 by 001 gives 100001100100001100001100100001...

%H Clark Kimberling, <a href="/A287801/b287801.txt">Table of n, a(n) for n = 1..10000</a>

%t s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 10] (* A003849 *)

%t w = StringJoin[Map[ToString, s]]

%t w1 = StringReplace[w, {"0" -> "100", "1" -> "001"}]

%t st = ToCharacterCode[w1] - 48 (* A287801 *)

%t Flatten[Position[st, 0]] (* A287802 *)

%t Flatten[Position[st, 1]] (* A287803 *)

%Y Cf. A287802, A287803.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 03 2017