A288466 Fixed point of the mapping 00->0101, 1->010, starting with 00.

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

Offset

1

Comments

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288260(n).

Links

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

Example

Iterates, starting with 00:
00
0101
00100010
0101010010100100
0010001000100101010001001010100101

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "1" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288466 *)
Flatten[Position[st, 0]]  (* A288467 *)
Flatten[Position[st, 1]]  (* A288468 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288260 conjectured *)

Crossrefs

Cf. A288467, A288468, A288260.

Sequence in context: A288524 A112416 A061265 * A285073 A276394 A215532

Adjacent sequences: A288463 A288464 A288465 * A288467 A288468 A288469

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2017

Status

approved