A288473 - OEIS

%I #9 Apr 06 2020 19:18:24

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

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

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

%N 1-limiting word of the mapping 00->0101, 1->011, starting with 00.

%C Iterates, starting with 00:

%C 00

%C 0101

%C 00110011

%C 01010110110101011011

%C 00110011001101100110110011001100110110011011

%C The 1-limiting word is the limit taken over odd-numbered iterations of the mapping.

%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288476(n).

%H Clark Kimberling, <a href="/A288473/b288473.txt">Table of n, a(n) for n = 1..10000</a>

%e First two odd-numbered iterates of the mapping:

%e 0101

%e 01010110110101011011

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "011"}]

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

%t st = ToCharacterCode[w[11]] - 48   (* A288473 *)

%t Flatten[Position[st, 0]]  (* A288474 *)

%t Flatten[Position[st, 1]]  (* A288475 *)

%t Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)

%Y Cf. A288474, A288475, A288476, A288551 (0-limiting word).

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 11 2017