A288259 -id:A288259

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A288258

Positions of 0 in A288257; complement of A288259.

+20
3

1, 2, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 34, 36, 37, 38, 39, 41, 42, 43, 45, 47, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 83, 85, 86, 87, 88, 90

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Conjecture: a(n)/n-> 1.36..., and if m denotes this number, then -1 < m - a(n)/n < 1 for n >= 1.

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" -> "0010", "1" -> "100"}]

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

st = ToCharacterCode[w[11]] - 48 (* A288257 *)

Flatten[Position[st, 0]] (* A288258 *)

Flatten[Position[st, 1]] (* A288259 *)

CROSSREFS

Cf. A288257, A288259.

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 09 2017

STATUS

approved

A288257

Fixed point of the mapping 00->0010, 1->100, starting with 00.

+10
4

0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

LINKS

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

EXAMPLE

Iterates, starting with 00:

0010

00101000

0010100010000100

0010100010000100100001000101000010