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%I #9 Apr 06 2020 19:18:24
%S 0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,
%T 0,1,1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,
%U 0,1,1,0,1,1,0,1,0,1,0,1,1,0,1,1,0,0
%N 1-limiting word of the mapping 00->0101, 1->011, starting with 00.
%C Iterates, starting with 00:
%C 00
%C 0101
%C 00110011
%C 01010110110101011011
%C 00110011001101100110110011001100110110011011
%C The 1-limiting word is the limit taken over odd-numbered iterations of the mapping.
%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288476(n).
%H Clark Kimberling, <a href="/A288473/b288473.txt">Table of n, a(n) for n = 1..10000</a>
%e First two odd-numbered iterates of the mapping:
%e 0101
%e 01010110110101011011
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "011"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]] - 48 (* A288473 *)
%t Flatten[Position[st, 0]] (* A288474 *)
%t Flatten[Position[st, 1]] (* A288475 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)
%Y Cf. A288474, A288475, A288476, A288551 (0-limiting word).
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 11 2017
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