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A288936 Fixed point of the mapping 00->0010, 01->011, 10->011, starting with 00. 3
0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1 (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 A000124.

LINKS

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

FORMULA

The first six iterates of the mapping:

00

0010

0010011

00100110111

0010011011011111

0010011011011101111111

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" -> "011"}]

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

st = ToCharacterCode[w[z]] - 48   (* A288936 *)

Flatten[Position[st, 0]]  (* A288937 *)

Flatten[Position[st, 1]]  (* A288938 *)

Table[StringLength[w[n]], {n, 0, 20}] (* A000124 conjectured *)

CROSSREFS

Cf. A000124, A288937, A288938.

Sequence in context: A289057 A106138 A273129 * A064990 A284388 A289174

Adjacent sequences:  A288933 A288934 A288935 * A288937 A288938 A288939

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 28 2017

STATUS

approved

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Last modified December 13 03:41 EST 2019. Contains 329968 sequences. (Running on oeis4.)