A288478 Fixed point of the mapping 00->0101, 1->110, starting with 00.

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

Offset

1

Comments

Iterates, starting with 00:

00

0101

01100110

011011001011101100

011011001101100101110011011011001101100101

Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A182780(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" -> "0101", "1" -> "110"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288478 *)
Flatten[Position[st, 0]]  (* A288479 *)
Flatten[Position[st, 1]]  (* A288480 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A182780 conjectured *)

Crossrefs

Cf. A288479, A288480, A182780.

Sequence in context: A284627 A322829 A286400 * A225183 A082410 A189479

Adjacent sequences: A288475 A288476 A288477 * A288479 A288480 A288481

Keyword

nonn,easy

Author

Clark Kimberling, Jun 12 2017

Status

approved