A288926 1-limiting word of the mapping 00->1000, 10->0001, starting with 00.

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

Offset

1

Comments

Iterates of the mapping, starting with 00:

00

1000

00011000

10000100011000

00011000000011000100011000

100001000110001000100010001100000011000100011000

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 2.

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288925(n), for n >= 0.

Links

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

Example

The first three iterates for n == 1 mod 2:
1000
10000100011000
100001000110001000100010001100000011000100011000

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "0001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[53]] - 48   (* A288926 *)
Flatten[Position[st, 0]]  (* A288927 *)
Flatten[Position[st, 1]]  (* A288928 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A288925 *)

Crossrefs

Cf. A288710 (0-limiting word), A288927, A288928, A288925.

Sequence in context: A378215 A288220 A173856 * A373840 A027356 A361114

Adjacent sequences: A288923 A288924 A288925 * A288927 A288928 A288929

Keyword

nonn,easy

Author

Clark Kimberling, Jun 25 2017

Status

approved