A289242 Fixed point of the mapping 00->0010, 01->100, 10->100, starting with 00.

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

Offset

1

Comments

Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289004.

Links

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

Example

The first six iterates of the mapping:
00
0010
0010100
00101001000
001010010010000100
0010100100100001010000101000010

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" -> "100"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289242 *)
Flatten[Position[st, 0]]  (* A289243 *)
Flatten[Position[st, 1]]  (* A289244 *)
Table[StringLength[w[n]], {n, 0, 20}] (* A289004 *)

Crossrefs

Cf. A289243, A289244, A289004.

Sequence in context: A289071 A287931 A289074 * A346218 A188037 A144598

Adjacent sequences: A289239 A289240 A289241 * A289243 A289244 A289245

Keyword

nonn,easy

Author

Clark Kimberling, Jul 01 2017

Status

approved