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Fixed point of the mapping 00->0010, 1->100, starting with 00.
4

%I #5 Jun 08 2017 18:21:25

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

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

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

%N Fixed point of the mapping 00->0010, 1->100, starting with 00.

%H Clark Kimberling, <a href="/A288257/b288257.txt">Table of n, a(n) for n = 1..10000</a>

%e Iterates, starting with 00:

%e 00

%e 0010

%e 00101000

%e 0010100010000100

%e 0010100010000100100001000101000010

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "1" -> "100"}]

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

%t st = ToCharacterCode[w[11]] - 48 (* A288257 *)

%t Flatten[Position[st, 0]] (* A288258 *)

%t Flatten[Position[st, 1]] (* A288259 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288260 conjectured *)

%Y Cf. A288258, A288259, A288260.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 07 2017