A288673 - OEIS

%I #9 Apr 06 2020 19:41:55

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

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

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

%N 2-limiting word of the mapping 00->0110, 10->000, starting with 00.

%C Iterates of the mapping, starting with 00:

%C 00

%C 0110

%C 01000

%C 00000110

%C 0110011001000

%C 010000100000000110

%C 00000110000001100110011001000

%C 01100110010000110011001000010000100000000110

%C The 2-limiting word is the limit of the n-th iterates for n == 2 mod 3. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).

%H Clark Kimberling, <a href="/A288673/b288673.txt">Table of n, a(n) for n = 1..10000</a>

%e The first two n-th iterates for n == 2 mod 3 are

%e 01000

%e 010000100000000110

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]

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

%t st = ToCharacterCode[w[14]] - 48   (* A288673 *)

%t Flatten[Position[st, 0]]  (* A288674 *)

%t Flatten[Position[st, 1]]  (* A288675 *)

%Y Cf. A288665 (0-limiting word), A288670 (2-limiting word), A288674, A288675.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 15 2017