A288600 Fixed point of the mapping 00->0101, 10->1001, starting with 00.

0, 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

Offset

1

Comments

Iterates, starting with 00:

00

0101

010011

01001011

010010100111

010010100110010111

0100101001100101100101001111

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288603(n).

Is this A288375 with a prefixed 0? - R. J. Mathar, Nov 04 2017

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" -> "0101", "10" -> "1001"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288600 *)
Flatten[Position[st, 0]]  (* A288601 *)
Flatten[Position[st, 1]]  (* A288602 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288603 conjectured *)

Crossrefs

Cf. A288601, A288602, A288603.

Sequence in context: A085242 A059620 A188014 * A284468 A260455 A189572

Adjacent sequences: A288597 A288598 A288599 * A288601 A288602 A288603

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2017

Extensions

Definition corrected by Georg Fischer, May 28 2021

Status

approved