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A288733 1-limiting word of the mapping 00->1000, 10->01, starting with 00. 6
1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

00

1000

011000

01011000

0011011000

10001011011000

011000011011011000

0101100001011011011000

00110110000011011011011000

1000101101100010001011011011011000

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 4.  Conjecture: the number of letters (0s and 1s) in the n-th iterate is given by A288732(n), for n >= 0.

LINKS

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

EXAMPLE

The first three n-th iterates for n == 1 mod 3 are

1000

10001011011000

1000101101100010001011011011011000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}]

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

st = ToCharacterCode[w[21]] - 48   (* A288733 *)

Flatten[Position[st, 0]]  (* A288734 *)

Flatten[Position[st, 1]]  (* A288735 *)

Table[StringLength[w[n]], {n, 0, 20}] (* A288732 *)

CROSSREFS

Cf. A288729 (0-limiting word), A288734, A288735, A288732,  A288736 (2-limiting word), A288741 (3-limiting word).

Sequence in context: A266444 A267679 A267868 * A095111 A166253 A159638

Adjacent sequences:  A288730 A288731 A288732 * A288734 A288735 A288736

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 16 2017

STATUS

approved

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Last modified March 26 12:43 EDT 2019. Contains 321497 sequences. (Running on oeis4.)