A288670 1-limiting word of the mapping 00->0110, 10->000, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

0110

01000

00000110

0110011001000

010000100000000110

00000110000001100110011001000

01100110010000110011001000010000100000000110

The 1-limiting word is the limit of the n-th iterates for n == 1 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 three n-th iterates for n == 1 mod 3 are
0110
0110011001000
01100110010000110011001000010000100000000110

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[13]] - 48   (* A288670 *)
Flatten[Position[st, 0]]  (* A288671 *)
Flatten[Position[st, 1]]  (* A288672 *)

Crossrefs

Cf. A288665 (0-limiting word), A288671, A288672, A288673 (2-limiting word).

Sequence in context: A287657 A347198 A079336 * A057215 A284905 A291197

Adjacent sequences: A288667 A288668 A288669 * A288671 A288672 A288673

Keyword

nonn,easy

Author

Clark Kimberling, Jun 15 2017

Status

approved