A288257 Fixed point of the mapping 00->0010, 1->100, starting with 00.

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

Offset

1

Links

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

Example

Iterates, starting with 00:
00
0010
00101000
0010100010000100
0010100010000100100001000101000010

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "1" -> "100"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288257 *)
Flatten[Position[st, 0]]  (* A288258 *)
Flatten[Position[st, 1]]  (* A288259 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288260 conjectured *)

Crossrefs

Cf. A288258, A288259, A288260.

Sequence in context: A260445 A156731 A254379 * A285666 A120325 A285139

Adjacent sequences: A288254 A288255 A288256 * A288258 A288259 A288260

Keyword

nonn,easy

Author

Clark Kimberling, Jun 07 2017

Status

approved