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A288665 0-limiting word of the mapping 00->0110, 10->000, starting with 00. 6
0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

  00

  0110

  01000

  00000110

  0110011001000

  010000100000000110

  00000110000001100110011001000

  01100110010000110011001000010000100000000110

The 0-limiting word is the limit of the n-th iterates for n == 0 mod 3.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).

LINKS

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

EXAMPLE

The first three n-th iterates for n == 0 mod 3 are

  00

  00000110

  00000110000001100110011001000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]

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

st = ToCharacterCode[w[9]] - 48   (* A288665 *)

Flatten[Position[st, 0]]  (* A288666 *)

Flatten[Position[st, 1]]  (* A288667 *)

Table[StringLength[w[n]], {n, 0, 20}] (* A288668 conjectured *)

CROSSREFS

Cf. A288666, A288667, A288668, A299670 (1-limiting word), A299673 (2-limiting word).

Sequence in context: A011667 A144195 A226464 * A011759 A316345 A118952

Adjacent sequences:  A288662 A288663 A288664 * A288666 A288667 A288668

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 15 2017

STATUS

approved

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Last modified January 25 03:44 EST 2022. Contains 350565 sequences. (Running on oeis4.)