%I
%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"}] (*ThueMorse 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
