A288932 Fixed point of the mapping 00->1000, 10->10101, starting with 00.

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

Offset

1

Comments

Conjecture: The number of letters (0's and 1's) in the n-th iterate of the mapping is given by A123720.

The first five iterates of the mapping:

00

1000

101011000

10101101011101011000

1010110101110101101011110101101011101011000

No iterate is an initial subword of its successor.

Links

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

Michel Dekking, A288932 A308185 connection

Formula

a(n+1) = A308185(n). - Michel Dekking, Feb 15 2021

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "10101"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288932 *)
Flatten[Position[st, 0]]  (* A288933 *)
Flatten[Position[st, 1]]  (* A288934 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A123720 conjectured *)

Crossrefs

Cf. A288933, A288934, A123720, A308185.

Sequence in context: A131670 A188044 A287523 * A155482 A174205 A334413

Adjacent sequences: A288929 A288930 A288931 * A288933 A288934 A288935

Keyword

nonn,easy

Author

Clark Kimberling, Jun 25 2017

Extensions

Corrected by Clark Kimberling, Feb 13 2021

Status

approved