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A288508 0-limiting word of the mapping 00->0101, 10->001, starting with 00. 4
0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Iterates, starting with 00:

00

0101

00011

0101011

000100111

010100010111

00010010101001111

01010001000100100101111

000100101010010101001000100011111

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 A288511(n).

LINKS

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

EXAMPLE

The first 5 even-numberd iterates:

00

00011

000100111

00010010101001111

000100101010010101001000100011111

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "001"}]

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

st = ToCharacterCode[w[18]] - 48   (* A288508 *)

Flatten[Position[st, 0]]  (* A288509 *)

Flatten[Position[st, 1]]  (* A288510 *)

Table[StringLength[w[n]], {n, 1, 35}] (* A288511 conjectured *)

CROSSREFS

Cf. A288509, A288510, A288511.

Sequence in context: A320927 A134391 A102215 * A262588 A234577 A038189

Adjacent sequences:  A288505 A288506 A288507 * A288509 A288510 A288511

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 12 2017

STATUS

approved

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Last modified August 5 07:21 EDT 2020. Contains 336209 sequences. (Running on oeis4.)