A287657 - OEIS

%I #5 Jun 02 2017 15:01:20

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

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

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

%N {0->01, 1->10}-transform of the infinite Fibonacci word A003849.

%H Clark Kimberling, <a href="/A287657/b287657.txt">Table of n, a(n) for n = 1..10000</a>

%e As a word, A003849 = 0100101001001010010100100..., and replacing each 0 by 01 and each 1 by 10 gives 01100101100110010110010110011001...

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

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

%t w1 = StringReplace[w, {"0" -> "01", "1" -> "10"}]   (*Thue-Morse transform*)

%t st = ToCharacterCode[w1] - 48    (*A287657*)

%t Flatten[Position[st, 0]]  (*A287658*)

%t Flatten[Position[st, 1]]  (*A287659*)

%Y Cf. A003849, A287658, A287659.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 02 2017