A286807 Fixed point of the mapping 00->001, 1->101, starting with 00.

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

Offset

1

Comments

Conjecture: The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A132045.

Links

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

Example

Iterates, starting with 00:
00
001
001101
0011011010101
0011011010101101010101010101
00110110101011010101010101011010101010101010101010101010101

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "101"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A286807 *)
Flatten[Position[st, 0]]  (* A286808 *)
Flatten[Position[st, 1]]  (* A286809 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A132045 conjectured *)

Crossrefs

Cf. A286808, A286809, A132045.

Sequence in context: A380173 A288729 A335617 * A126564 A180433 A358771

Adjacent sequences: A286804 A286805 A286806 * A286808 A286809 A286810

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2017

Status

approved