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

Offset

1,1

Comments

Conjecture: a(n)/n -> (3 + sqrt(5))/2 = 1 + golden ratio = 1 + tau, and 1 + tau < 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}]]
st = ToCharacterCode[w[z]] - 48   (* A289104 *)
Flatten[Position[st, 0]]  (* A289105 *)
Flatten[Position[st, 1]]  (* A289106 *)

Crossrefs

Cf. A001622, A289104, A289105, A289106.

Sequence in context: A357628 A289151 A085776 * A289018 A316672 A288993

Adjacent sequences: A289103 A289104 A289105 * A289107 A289108 A289109

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved