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A286807 Fixed point of the mapping 00->001, 1->101, starting with 00. 3
0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 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 A132045.

LINKS

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

EXAMPLE

Iterates, starting with 00:

00

001

001101

0011011010101

0011011010101101010101010101

00110110101011010101010101011010101010101010101010101010101

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "001", "1" -> "101"}]

Table[w[n], {n, 0, 8}]

st = ToCharacterCode[w[11]] - 48   (* A286807 *)

Flatten[Position[st, 0]]  (* A286808 *)

Flatten[Position[st, 1]]  (* A286809 *)

Table[StringLength[w[n]], {n, 1, 35}] (* A132045 conjectured *)

CROSSREFS

Cf. A286808, A286809, A132045.

Sequence in context: A062301 A181712 A288729 * A126564 A180433 A165560

Adjacent sequences:  A286804 A286805 A286806 * A286808 A286809 A286810

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2017

STATUS

approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)