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 A288377 Fixed point of the mapping 00->0001, 1->10, starting with 00. 4

%I

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

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

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

%N Fixed point of the mapping 00->0001, 1->10, starting with 00.

%H Clark Kimberling, <a href="/A288377/b288377.txt">Table of n, a(n) for n = 1..10000</a>

%e Iterates, starting with 00:

%e 00

%e 0001

%e 0001010

%e 00010100100

%e 00010100100001100001

%e 00010100100001100001000110100001000110

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0001", "1" -> "10"}]

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

%t st = ToCharacterCode[w[11]] - 48 (* A288377 *)

%t Flatten[Position[st, 0]] (* A288378 *)

%t Flatten[Position[st, 1]] (* A288379 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288380 conjectured *)

%Y Cf. A288378, A288379, A288380.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 09 2017

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Last modified January 22 11:06 EST 2022. Contains 350481 sequences. (Running on oeis4.)