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A289128 Fixed point of the mapping 00->0010, 01->011, 10->010, starting with 00. 5
0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 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 A289131.

LINKS

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

EXAMPLE

The first six iterates of the mapping:

00

0010

0010010

00100100110

001001001100101010

0010010011001010100110110110

MATHEMATICA

z = 11; (* number of iterates *)

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

w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "011", "10" -> "010"}]

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

st = ToCharacterCode[w[z]] - 48   (* A289128 *)

Flatten[Position[st, 0]]  (* A289129 *)

Flatten[Position[st, 1]]  (* A289130 *)

Table[StringLength[w[n]], {n, 0, 20}] (* A289131 conjectured *)

CROSSREFS

Cf. A289129, A289130, A289131.

Sequence in context: A340507 A072785 A188297 * A272664 A074937 A143518

Adjacent sequences:  A289125 A289126 A289127 * A289129 A289130 A289131

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 28 2017

STATUS

approved

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)