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A288551 0-limiting word of the mapping 00->0101, 1->011, starting with 00. 4
0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates, starting with 00:

00

0101

00110011

01010110110101011011

00110011001101100110110011001100110110011011

The 0-limiting word is the limit taken over even-numbered iterations of the mapping.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288476(n).

LINKS

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

EXAMPLE

First three even-numbered iterates of the mapping:

00

00110011

00110011001101100110110011001100110110011011

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "011"}]

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

st = ToCharacterCode[w[10]] - 48   (* A288551 *)

Flatten[Position[st, 0]]  (* A288552 *)

Flatten[Position[st, 1]]  (* A288553 *)

Table[StringLength[w[n]], {n, 1, 35}] (* A288476 conjectured *)

CROSSREFS

Cf. A288552, A288553, A288476, A288473 (the 1-limiting word).

Sequence in context: A132380 A021913 A285501 * A327174 A269723 A284487

Adjacent sequences:  A288548 A288549 A288550 * A288552 A288553 A288554

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 14 2017

STATUS

approved

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Last modified July 2 16:47 EDT 2020. Contains 335404 sequences. (Running on oeis4.)