A285666 Fixed point of the mapping 00->001, 1->010, starting with 00.

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

Offset

1

Comments

Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A001580.

Links

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

Example

Iterates, starting with 00:
00
001
001010
00101000100
00101000100010010001
0010100010001001000100100010100010010

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "010"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A285666 *)
Flatten[Position[st, 0]]  (* A285667 *)
Flatten[Position[st, 1]]  (* A286058 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A001580 conjectured *)

Crossrefs

Cf. A285667, A286058, A001580.

Sequence in context: A156731 A254379 A288257 * A120325 A285139 A289011

Adjacent sequences: A285663 A285664 A285665 * A285667 A285668 A285669

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2017

Status

approved