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0-limiting word of the mapping 00->0110, 1->01, starting with 00.
3

%I #7 Apr 07 2020 21:05:58

%S 0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,0,0,1,

%T 0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,

%U 0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0

%N 0-limiting word of the mapping 00->0110, 1->01, starting with 00.

%C Iterates, starting with 00:

%C 00

%C 0110

%C 001010

%C 0110010010

%C 001010110010110010

%C 01100100100101011001001010110010\

%C 0010101100101100101100100100101011001011001001001010110010

%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288465(n).

%H Clark Kimberling, <a href="/A288752/b288752.txt">Table of n, a(n) for n = 1..10000</a>

%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "1" -> "01"}]

%t Table[w[n], {n, 0, 8}]

%t st = ToCharacterCode[w[11]] - 48 (* A288752 *)

%t Flatten[Position[st, 0]] (* A288753 *)

%t Flatten[Position[st, 1]] (* A288754 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288465 conjectured *)

%Y Cf. A288622 (0- word), A288753, A288754, A288465.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 15 2017