A286063 - OEIS

%I #6 Apr 06 2020 20:23:11

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

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

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

%N Fixed point of the mapping 00->001, 1->100, starting with 00.

%C The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A042950.

%H Clark Kimberling, <a href="/A286063/b286063.txt">Table of n, a(n) for n = 1..10000</a>

%e Iterates, starting with 00:

%e 00

%e 001

%e 001100

%e 001100100001

%e 001100100001100001001100

%e 001100100001100001001100100001001100001100100001

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "100"}]

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

%t st = ToCharacterCode[w[11]] - 48   (* A286063 *)

%t Flatten[Position[st, 0]]  (* A286727 *)

%t Flatten[Position[st, 1]]  (* A286728 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A042950 *)

%Y Cf. A286727, A286728, A042950.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 05 2017