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A288929 Fixed point of the mapping 00->1000, 10->10011, starting with 00. 3
1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 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 A192967(n+2) for n >= 0.

Iterates, starting with 00:

00

1000

100111000

10011011100111000

1001101100111110011011100111000

100110110011110011011111001101100111110011011100111000

No iterate is an initial subword of its successor.

LINKS

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

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "10011"}]

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

st = ToCharacterCode[w[11]] - 48   (* A288929 *)

Flatten[Position[st, 0]]  (* A288930 *)

Flatten[Position[st, 1]]  (* A288931 *)

Table[StringLength[w[n]], {n, 1, 35}] (* A192967 conjectured *)

CROSSREFS

Cf. A288930, A288931, A192967.

Sequence in context: A083035 A187074 A188398 * A285083 A266982 A051341

Adjacent sequences:  A288926 A288927 A288928 * A288930 A288931 A288932

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 25 2017

EXTENSIONS

Definition corrected by Georg Fischer, May 28 2021

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)