Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%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