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A289239 Fixed point of the mapping 00->0010, 01->100, 10->010, starting with 00. 3
0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Conjecture: the number of letters (0's and 1's) in the n-th iterate of the mapping is given by A289004.

LINKS

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

EXAMPLE

The first six iterates of the mapping:

00

0010

0010010

00100101000

001001010010000100

0010010100100001001000101000010

MATHEMATICA

z = 11; (* number of iterates *)

s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];

w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "100", "10" -> "010"}]

TableForm[Table[w[n], {n, 0, 10}]]

st = ToCharacterCode[w[z]] - 48   (* A289239 *)

Flatten[Position[st, 0]]  (* A289240 *)

Flatten[Position[st, 1]]  (* A289241 *)

Table[StringLength[w[n]], {n, 0, 20}] (* A289004 conjectured *)

CROSSREFS

Cf. A289240, A289241, A289004.

Sequence in context: A122414 A288216 A189628 * A188432 A282317 A212126

Adjacent sequences:  A289236 A289237 A289238 * A289240 A289241 A289242

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 29 2017

STATUS

approved

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Last modified May 11 06:28 EDT 2021. Contains 343784 sequences. (Running on oeis4.)