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A288858 2-limiting word of the mapping 00->1000, 10->011, starting with 00. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A029693 A200263 A051067 * A190897 A309218 A189718

Adjacent sequences:  A288855 A288856 A288857 * A288859 A288860 A288861

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 23 2017

STATUS

approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)