%I
%S 0,0,1,1,0,0,0,0,0,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,1,0,
%T 0,0,1,0,0,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,1,1,0,0,0,
%U 1,0,0,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0
%N 0limiting word of the mapping 00>1000, 10>001, starting with 00.
%C Iterates of the mapping, starting with 00:
%C 00
%C 1000
%C 0011000
%C 100010011000
%C 0011000001010011000
%C 1000100110001000001001010011000
%C 0011000001010011000001100010000010001001010011000
%C The 0limiting word is the limit of the nth iterates for even n.
%C Conjecture: the number of letters (0's and 1's) in the nth iterate is given by A287525(n), for n >= 0.
%H Clark Kimberling, <a href="/A287382/b287382.txt">Table of n, a(n) for n = 1..10000</a>
%e The first four nth iterates for even n:
%e 00
%e 0011000
%e 0011000001010011000
%e 0011000001010011000001100010000010001001010011000
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n  1], {"00" > "1000", "10" > "001"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[23]]  48 (* A287382 *)
%t Flatten[Position[st, 0]] (* A287440 *)
%t Flatten[Position[st, 1]] (* A287448 *)
%t v = Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)
%Y Cf. A287440, A287448, A287525, A287530 (1limiting word).
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 18 2017
