A288929 Fixed point of the mapping 00->1000, 10->10011, starting with 00.

1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 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 A192967(n+2) for n >= 0.

Iterates, starting with 00:

00

1000

100111000

10011011100111000

1001101100111110011011100111000

100110110011110011011111001101100111110011011100111000

No iterate is an initial subword of its successor.

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" -> "1000", "10" -> "10011"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288929 *)
Flatten[Position[st, 0]]  (* A288930 *)
Flatten[Position[st, 1]]  (* A288931 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A192967 conjectured *)

Crossrefs

Cf. A288930, A288931, A192967.

Sequence in context: A356161 A187074 A188398 * A285083 A266982 A364746

Adjacent sequences: A288926 A288927 A288928 * A288930 A288931 A288932

Keyword

nonn,easy

Author

Clark Kimberling, Jun 25 2017

Extensions

Definition corrected by Georg Fischer, May 28 2021

Status

approved