A288596 Fixed point of the mapping 00->0101, 10->1000, starting with 00.

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

Offset

1

Links

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

Example

Iterates, starting with 00:
00
0101
010001
0100001011
0100001010100011
0100001010100010001000010111
Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288599(n).

Mathematica

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "1000"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48   (* A288596 *)
Flatten[Position[st, 0]]  (* A288597 *)
Flatten[Position[st, 1]]  (* A288598 *)
Table[StringLength[w[n]], {n, 1, 35}] (* A288599 conjectured *)

Crossrefs

Cf. A288597, A288598, A288599.

Sequence in context: A132151 A370124 A238469 * A284745 A103588 A153638

Adjacent sequences: A288593 A288594 A288595 * A288597 A288598 A288599

Keyword

nonn,easy

Author

Clark Kimberling, Jun 14 2017

Extensions

Definition corrected by Georg Fischer, May 28 2021

Status

approved