A285666 - OEIS

%I #8 Apr 06 2020 20:21:16

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

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

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

%N Fixed point of the mapping 00->001, 1->010, starting with 00.

%C Conjecture:  the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A001580.

%H Clark Kimberling, <a href="/A285666/b285666.txt">Table of n, a(n) for n = 1..10000</a>

%e Iterates, starting with 00:

%e 00

%e 001

%e 001010

%e 00101000100

%e 00101000100010010001

%e 0010100010001001000100100010100010010

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "010"}]

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

%t st = ToCharacterCode[w[11]] - 48   (* A285666 *)

%t Flatten[Position[st, 0]]  (* A285667 *)

%t Flatten[Position[st, 1]]  (* A286058 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A001580 conjectured *)

%Y Cf. A285667, A286058, A001580.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 05 2017