A288375 Fixed point of the mapping 00->1000, 10->1001, starting at 00.

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

Offset

1

Comments

The first 5 iterates of the mapping:

00

1000

10011000

100010110011000

100101001110010110011000

No iterate is an initial subword of its successor.

Links

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

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "1001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[24]] - 48;   (* A288375 *)
p0 = Flatten[Position[st, 0]];  (* A288625 *)
p1 = Flatten[Position[st, 1]];  (* A283794 *)
Table[StringLength[w[n]], {n, 0, 30}] (* A019274 *)

Crossrefs

Cf. A288625, A283794, A019274.

Sequence in context: A359764 A065043 A189298 * A121559 A004641 A266441

Adjacent sequences: A288372 A288373 A288374 * A288376 A288377 A288378

Keyword

nonn,easy

Author

Clark Kimberling, Jun 24 2017

Extensions

Definition corrected by Georg Fischer, Jul 18 2019

Status

approved