A288600 - OEIS

%I #12 May 28 2021 11:06:08

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

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

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

%N Fixed point of the mapping 00->0101, 10->1001, starting with 00.

%C Iterates, starting with 00:

%C 00

%C 0101

%C 010011

%C 01001011

%C 010010100111

%C 010010100110010111

%C 0100101001100101100101001111

%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288603(n).

%C Is this A288375 with a prefixed 0? - _R. J. Mathar_, Nov 04 2017

%H Clark Kimberling, <a href="/A288600/b288600.txt">Table of n, a(n) for n = 1..10000</a>

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "1001"}]

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

%t st = ToCharacterCode[w[11]] - 48   (* A288600 *)

%t Flatten[Position[st, 0]]  (* A288601 *)

%t Flatten[Position[st, 1]]  (* A288602 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288603 conjectured *)

%Y Cf. A288601, A288602, A288603.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 14 2017

%E Definition corrected by _Georg Fischer_, May 28 2021