A287530 - OEIS

%I #8 Apr 06 2020 20:17:06

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

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

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

%N 1-limiting word of the mapping 00->1000, 10->001, starting with 00.

%C Iterates of the mapping, starting with 00:

%C 00

%C 1000

%C 0011000

%C 100010011000

%C 0011000001010011000

%C 1000100110001000001001010011000

%C 0011000001010011000001100010000010001001010011000

%C The 1-limiting word is the limit of the n-th iterates for odd n.

%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A287525(n), for n >= 0.

%H Clark Kimberling, <a href="/A287530/b287530.txt">Table of n, a(n) for n = 1..10000</a>

%e The first three n-th iterates for even n:

%e 1000

%e 100010011000

%e 1000100110001000001001010011000

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "001"}]

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

%t st = ToCharacterCode[w[23]] - 48   (* A287530 *)

%t Flatten[Position[st, 0]]  (* A287531 *)

%t Flatten[Position[st, 1]]  (* A287551 *)

%t Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)

%Y Cf. A287382 (0-limiting word), A287531, A287551, A287525.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 18 2017