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A287457 1-limiting word of the mapping 00->1000, 10->000, starting with 00. 5
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

00

1000

0001000

100000001000

0001000100010000001000

10000000100000010000001000100000001000

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

Conjecture: the number of letters (0s and 1s) in the n-th iterate is given by A287439(n), for n >= 0.

See comments of A287372 for a proof of this conjecture. - Michel Dekking, Mar 19 2018

LINKS

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

EXAMPLE

The first three n-th iterates for odd n:

1000

100000001000

10000000100000010000001000100000001000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "000"}]

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

st = ToCharacterCode[w[23]] - 48   (* A287457 *)

Flatten[Position[st, 0]]  (* A287519 *)

Flatten[Position[st, 1]]  (* A287186 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A287439 *)

CROSSREFS

Cf. A287372 (0-limiting word), A287519, A287186, A287439.

Sequence in context: A253513 A014025 A279760 * A324917 A285898 A185118

Adjacent sequences:  A287454 A287455 A287456 * A287458 A287459 A287460

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 17 2017

STATUS

approved

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Last modified October 17 16:31 EDT 2019. Contains 328117 sequences. (Running on oeis4.)