A289104 Fixed point of the mapping 00->0010, 01->011, 10->000, starting with 00.

0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 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 A289107. For connections to the golden ratio, see A289105 and A289106.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010000
001000000100
0010000001000100110010
0010000001000100110010011001010000110

Mathematica

z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "011", "10" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289104 *)
Flatten[Position[st, 0]]  (* A289105 *)
Flatten[Position[st, 1]]  (* A289106 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289107 *)

Crossrefs

Cf. A001622, A289105, A289106, A289107.

Sequence in context: A288167 A288991 A289016 * A289235 A188371 A353489

Adjacent sequences: A289101 A289102 A289103 * A289105 A289106 A289107

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved