A288673 2-limiting word of the mapping 00->0110, 10->000, starting with 00.

0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 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, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

0110

01000

00000110

0110011001000

010000100000000110

00000110000001100110011001000

01100110010000110011001000010000100000000110

The 2-limiting word is the limit of the n-th iterates for n == 2 mod 3. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288468(n).

Links

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

Example

The first two n-th iterates for n == 2 mod 3 are
01000
010000100000000110

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[14]] - 48   (* A288673 *)
Flatten[Position[st, 0]]  (* A288674 *)
Flatten[Position[st, 1]]  (* A288675 *)

Crossrefs

Cf. A288665 (0-limiting word), A288670 (2-limiting word), A288674, A288675.

Sequence in context: A356982 A284683 A369968 * A030213 A187969 A132151

Adjacent sequences: A288670 A288671 A288672 * A288674 A288675 A288676

Keyword

nonn,easy

Author

Clark Kimberling, Jun 15 2017

Status

approved