A288314 Fixed point of the mapping 00->0001, 1->00, starting with 00.

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

Offset

1

Links

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

Example

Iterates, starting with 00:
00
0001
0001000
000100000010
0001000000100010001000
0001000000100010001000001000000100000010

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0001", "1" -> "00"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288314 *)
Flatten[Position[st, 0]]  (* A288315 *)
Flatten[Position[st, 1]]  (* A288316 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288317 conjectured *)

Crossrefs

Cf. A288315, A288316, A288317.

Sequence in context: A369070 A024360 A025456 * A285963 A024889 A368701

Adjacent sequences: A288311 A288312 A288313 * A288315 A288316 A288317

Keyword

nonn,easy

Author

Clark Kimberling, Jun 09 2017

Status

approved