A289235 Fixed point of the mapping 00->0010, 01->100, 10->000, starting with 00.

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

Offset

1

Comments

The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289153.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010000
001000000100
0010000001000101000010
001000000100010100001010010000100010000

Mathematica

z = 11; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "000"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289235 *)
Flatten[Position[st, 0]]  (* A289002 *)
Flatten[Position[st, 1]]  (* A289151 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289153 *)

Crossrefs

Cf. A289002, A289151, A289153.

Sequence in context: A288991 A289016 A289104 * A188371 A353489 A288106

Adjacent sequences: A289232 A289233 A289234 * A289236 A289237 A289238

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved