A288736 2-limiting word of the mapping 00->1000, 10->01, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

011000

01011000

0011011000

10001011011000

011000011011011000

0101100001011011011000

00110110000011011011011000

1000101101100010001011011011011000

The 2-limiting word is the limit of the n-th iterates for n == 2 mod 4. Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288732(n), for n >= 0.

Links

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

Example

The first three n-th iterates for n == 2 mod 3 are
011000
011000011011011000
011000011011011000011000011011011011011000

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "01"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[22]] - 48   (* A288736 *)
Flatten[Position[st, 0]]  (* A288737 *)
Flatten[Position[st, 1]]  (* A288740 *)

Crossrefs

Cf. A288729 (0-limiting word), A288737, A288740, A288733 (1-limiting word), A288741 (3-limiting word).

Sequence in context: A125720 A095130 A284789 * A270803 A030301 A316341

Adjacent sequences: A288733 A288734 A288735 * A288737 A288738 A288739

Keyword

nonn,easy

Author

Clark Kimberling, Jun 16 2017

Status

approved