A288997 Fixed point of the mapping 00->0010, 01->001, 10->001, starting with 00.

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

Offset

1

Comments

The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289000.

Conjecture: a(n) = A171588(n+3) for all n>0. - Michel Dekking, Mar 21 2022

Links

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

Example

The first seven iterates of the mapping:
00
0010
0010001
001000100101
00100010010001001001
0010001001000100100100010010001001
0010001001000100100100010010001001001000100100010010001001

Mathematica

z = 10; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "001"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A288997 *)
Flatten[Position[st, 0]]  (* A288998 *)
Flatten[Position[st, 1]]  (* A288999 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289000 *)

Crossrefs

Cf. A288998, A288999, A289000.

Sequence in context: A073059 A288173 A221150 * A276794 A289025 A289112

Adjacent sequences: A288994 A288995 A288996 * A288998 A288999 A289000

Keyword

nonn,easy

Author

Clark Kimberling, Jun 25 2017

Status

approved