A288741 - OEIS

%I #10 Apr 07 2020 21:19:25

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

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

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

%N 3-limiting word of the mapping 00->1000, 10->01, starting with 00.

%C Iterates of the mapping, starting with 00:

%C 00

%C 1000

%C 011000

%C 01011000

%C 0011011000

%C 10001011011000

%C 011000011011011000

%C 0101100001011011011000

%C 00110110000011011011011000

%C 1000101101100010001011011011011000

%C The 3-limiting word is the limit of the n-th iterates for n == 3 mod 4.

%C Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288732(n), for n >= 0.

%H Clark Kimberling, <a href="/A288741/b288741.txt">Table of n, a(n) for n = 1..10000</a>

%e The first two n-th iterates for n == 3 mod 4 are

%e 01011000

%e 0101100001011011011000

%e 00110110000011011011011000

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

%t w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}]

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

%t st = ToCharacterCode[w[23]] - 48   (* A288741 *)

%t Flatten[Position[st, 0]]  (* A288742 *)

%t Flatten[Position[st, 1]]  (* A285697 *)

%Y Cf. A288729 (0-limiting word), A288732, A288733 (1-limiting word), A288736 (2-limiting word), A288742, A285697.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Jun 17 2017