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A288710 0-limiting word of the mapping 00->1000, 10->0001, starting with 00. 4
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates of the mapping, starting with 00:

00

1000

00011000

10000100011000

00011000000011000100011000

100001000110001000100010001100000011000100011000

The 0-limiting word is the limit of the n-th iterates for n == 0 mod 2.

Conjecture:  the number of letters (0's and 1's) in the n-th iterate is given by A288925(n), for n >= 0.

LINKS

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

EXAMPLE

The first three iterates for n == 0 mod 2:

00

00011000

00011000000011000100011000

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "0001"}]

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

st = ToCharacterCode[w[54]] - 48   (* A288710 *)

Flatten[Position[st, 0]]  (* A288711 *)

Flatten[Position[st, 1]]  (* A288755 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)

CROSSREFS

Cf. A288926 (1-limiting word), A288711, A288755, A288925.

Sequence in context: A137331 A093386 A219098 * A179827 A285133 A011658

Adjacent sequences:  A288707 A288708 A288709 * A288711 A288712 A288713

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 24 2017

STATUS

approved

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Last modified October 26 11:59 EDT 2021. Contains 348267 sequences. (Running on oeis4.)