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A287530 1-limiting word of the mapping 00->1000, 10->001, starting with 00. 4
1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

00

1000

0011000

100010011000

0011000001010011000

1000100110001000001001010011000

0011000001010011000001100010000010001001010011000

The 1-limiting word is the limit of the n-th iterates for odd n.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A287525(n), for n >= 0.

LINKS

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

EXAMPLE

The first three n-th iterates for even n:

1000

100010011000

1000100110001000001001010011000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "001"}]

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

st = ToCharacterCode[w[23]] - 48   (* A287530 *)

Flatten[Position[st, 0]]  (* A287531 *)

Flatten[Position[st, 1]]  (* A287551 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A287525 *)

CROSSREFS

Cf. A287382 (0-limiting word), A287531, A287551, A287525.

Sequence in context: A102243 A173859 A202108 * A104108 A190610 A267056

Adjacent sequences:  A287527 A287528 A287529 * A287531 A287532 A287533

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 18 2017

STATUS

approved

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Last modified May 11 02:34 EDT 2021. Contains 343784 sequences. (Running on oeis4.)