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%I A288670 #10 Apr 06 2020 19:41:12
%S A288670 0,1,1,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,0,
%T A288670 0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,
%U A288670 0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1
%N A288670 1-limiting word of the mapping 00->0110, 10->000, starting with 00.
%C A288670 Iterates of the mapping, starting with 00:
%C A288670 00
%C A288670 0110
%C A288670 01000
%C A288670 00000110
%C A288670 0110011001000
%C A288670 010000100000000110
%C A288670 00000110000001100110011001000
%C A288670 01100110010000110011001000010000100000000110
%C A288670 The 1-limiting word is the limit of the n-th iterates for n == 1 mod 3. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).
%H A288670 Clark Kimberling, <a href="/A288670/b288670.txt">Table of n, a(n) for n = 1..10000</a>
%e A288670 The first three n-th iterates for n == 1 mod 3 are
%e A288670 0110
%e A288670 0110011001000
%e A288670 01100110010000110011001000010000100000000110
%t A288670 s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t A288670 w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]
%t A288670 Table[w[n], {n, 0, 8}]
%t A288670 st = ToCharacterCode[w[13]] - 48   (* A288670 *)
%t A288670 Flatten[Position[st, 0]]  (* A288671 *)
%t A288670 Flatten[Position[st, 1]]  (* A288672 *)
%Y A288670 Cf. A288665 (0-limiting word), A288671, A288672, A288673 (2-limiting word).
%K A288670 nonn,easy
%O A288670 1
%A A288670 _Clark Kimberling_, Jun 15 2017

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