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A288855 1-limiting word of the mapping 00->1000, 10->011, starting with 00. 7
1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 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, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Iterates of the mapping, starting with 00:

00

1000

0111000

0110111000

01011110111000

0011111011110111000

10001111011111011110111000

01110001110111111011111011110111000

011011100011011111110111111011111011110111000

The 1-limiting word is the limit of the n-th iterates for n == 1 mod 5.

The number of letters (0's and 1's) in the n-th iterate is given by A288243(n), for n >= 0.

LINKS

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

EXAMPLE

The first two n-th iterates for n == 1 mod 5:  1000 and 10001111011111011110111000.  (The lengths of the first 10 such iterates are 4, 26, 87, 208, 417, 759, 1302, 2136, 3376, 5192.)

MATHEMATICA

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

w[n_] := StringReplace[w[n - 1], {"00" -> "1000", "10" -> "011"}]

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

st = ToCharacterCode[w[51]] - 48   (* A288855 *)

Flatten[Position[st, 0]]  (* A288856 *)

Flatten[Position[st, 1]]  (* A288857 *)

Table[StringLength[w[n]], {n, 0, 30}] (* A288243 *)

CROSSREFS

Cf. A288226 (0-limiting word), A288858 (2-limiting word), A288861 (3-limiting word), A288864 (4-limiting word), A288856, A288857, A288243.

Sequence in context: A284680 A004555 A200261 * A138711 A285617 A246500

Adjacent sequences:  A288852 A288853 A288854 * A288856 A288857 A288858

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 22 2017

STATUS

approved

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Last modified July 30 18:40 EDT 2021. Contains 346359 sequences. (Running on oeis4.)