A288508 0-limiting word of the mapping 00->0101, 10->001, starting with 00.

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

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