A288741 3-limiting word of the mapping 00->1000, 10->01, starting with 00.

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, 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, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

011000

01011000

0011011000

10001011011000

011000011011011000

0101100001011011011000

00110110000011011011011000

1000101101100010001011011011011000

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

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

The first two n-th iterates for n == 3 mod 4 are
01011000
0101100001011011011000
00110110000011011011011000

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[23]] - 48   (* A288741 *)
Flatten[Position[st, 0]]  (* A288742 *)
Flatten[Position[st, 1]]  (* A285697 *)

Crossrefs

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

Sequence in context: A353810 A115516 A285830 * A341684 A327183 A347870

Adjacent sequences: A288738 A288739 A288740 * A288742 A288743 A288744

Keyword

nonn,easy

Author

Clark Kimberling, Jun 17 2017

Status

approved