A288694 Fixed point of the mapping 00->0110, 10->100, starting with 00.

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

Offset

1

Comments

Iterates, starting with 00:

00

0110

01100

011000

011000110

0110001101100

011000110110011000

01100011011001100011000110

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288429(n).

Links

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

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0110", "10" -> "100"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288694 *)
Flatten[Position[st, 0]]  (* A288695 *)
Flatten[Position[st, 1]]  (* A288696 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288429 conjectured *)

Crossrefs

Cf. A288695, A288696, A288429.

Sequence in context: A093692 A254114 A105384 * A292077 A327256 A327177

Adjacent sequences: A288691 A288692 A288693 * A288695 A288696 A288697

Keyword

nonn,easy

Author

Clark Kimberling, Jun 16 2017

Status

approved