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A289001 Fixed point of the mapping 00->0010, 01->001, 10->010, starting with 00. 5
0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

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

Apparently a duplicate of A171588. The first 5000 entries (at least) are the same. - R. J. Mathar, Jul 07 2017

LINKS

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

EXAMPLE

The first seven iterates of the mapping:

00

0010

0010010

00100100010

001001000100100010

0010010001001000100100100010010

0010010001001000100100100010010001001001000100100010

MATHEMATICA

z = 10; (* number of iterates *)

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

w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "001", "10" -> "010"}]

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

st = ToCharacterCode[w[z]] - 48   (* A289001 *)

Flatten[Position[st, 0]]  (* A001951 conjectured *)

Flatten[Position[st, 1]]  (* A001952 conjectured *)

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

CROSSREFS

Cf. A001951, A001952, A289004.

Sequence in context: A288203 A238470 A286748 * A171588 A289035 A276397

Adjacent sequences:  A288998 A288999 A289000 * A289002 A289003 A289004

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 25 2017

STATUS

approved

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Last modified October 23 11:48 EDT 2019. Contains 328345 sequences. (Running on oeis4.)