%I
%S 0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,
%T 1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0,
%U 0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0
%N 2limiting word of the mapping 00>0110, 10>000, starting with 00.
%C Iterates of the mapping, starting with 00:
%C 00
%C 0110
%C 01000
%C 00000110
%C 0110011001000
%C 010000100000000110
%C 00000110000001100110011001000
%C 01100110010000110011001000010000100000000110
%C The 2limiting word is the limit of the nth iterates for n == 2 mod 3. Conjecture: the number of letters (0's and 1's) in the nth iterate is given by A288468(n).
%H Clark Kimberling, <a href="/A288673/b288673.txt">Table of n, a(n) for n = 1..10000</a>
%e The first two nth iterates for n == 2 mod 3 are
%e 01000
%e 010000100000000110
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n  1], {"00" > "0110", "10" > "000"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[14]]  48 (* A288673 *)
%t Flatten[Position[st, 0]] (* A288674 *)
%t Flatten[Position[st, 1]] (* A288675 *)
%Y Cf. A288665 (0limiting word), A288670 (2limiting word), A288674, A288675.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 15 2017
