Voozh

A289106

Positions of 1 in A289104; complement of A289105.

3, 10, 14, 17, 18, 21, 24, 25, 28, 30, 35, 36, 39, 41, 46, 47, 49, 50, 53, 57, 59, 64, 65, 67, 68, 71, 75, 77, 81, 86, 87, 90, 93, 94, 96, 97, 100, 104, 106, 110, 115, 116, 119, 122, 123, 125, 126, 129, 132, 133, 136, 140, 142, 147, 148, 151, 153, 157, 162

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

OFFSET

1,1

COMMENTS

Conjecture: a(n)/n -> (3 + sqrt(5))/2 = 1 + golden ratio = 1 + phi, and 1 + phi < a(n)/n < 4 for n >= 4.

LINKS

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

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" -> "000"}]

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