A288858 2-limiting word of the mapping 00->1000, 10->011, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

0111000

0110111000

01011110111000

0011111011110111000

10001111011111011110111000

01110001110111111011111011110111000

011011100011011111110111111011111011110111000

The 2-limiting word is the limit of the n-th iterates for n == 2 mod 5.

The number of letters (0's and 1's) in the n-th iterate is given by A288243(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 == 2 mod 5: 0111000 and 01110001110111111011111011110111000. (The lengths of the first 10 such iterates are 7, 35, 106, 242, 473, 849, 1442, 2346, 3685, 5642.)

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[52]] - 48   (* A288858 *)
Flatten[Position[st, 0]]  (* A288859 *)
Flatten[Position[st, 1]]  (* A288860 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)

Crossrefs

Cf. A288226 (0-limiting word), A288855 (1-limiting word), A288861 (3-limiting word), A288864 (4-limiting word), A288859, A288860, A288243.

Sequence in context: A373153 A051067 A379955 * A356313 A309218 A189718

Adjacent sequences: A288855 A288856 A288857 * A288859 A288860 A288861

Keyword

nonn,easy

Author

Clark Kimberling, Jun 23 2017

Status

approved