A288855 1-limiting word of the mapping 00->1000, 10->011, starting with 00.

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

Offset

1,1

Comments

Iterates of the mapping, starting with 00:

00

1000

0111000

0110111000

01011110111000

0011111011110111000

10001111011111011110111000

01110001110111111011111011110111000

011011100011011111110111111011111011110111000

The 1-limiting word is the limit of the n-th iterates for n == 1 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 == 1 mod 5:  1000 and 10001111011111011110111000.  (The lengths of the first 10 such iterates are 4, 26, 87, 208, 417, 759, 1302, 2136, 3376, 5192.)

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[51]] - 48   (* A288855 *)
Flatten[Position[st, 0]]  (* A288856 *)
Flatten[Position[st, 1]]  (* A288857 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)

Crossrefs

Cf. A288226 (0-limiting word), A288858 (2-limiting word), A288861 (3-limiting word), A288864 (4-limiting word), A288856, A288857, A288243.

Sequence in context: A284680 A004555 A200261 * A138711 A285617 A246500

Adjacent sequences: A288852 A288853 A288854 * A288856 A288857 A288858

Keyword

nonn,easy

Author

Clark Kimberling, Jun 22 2017

Status

approved