A289105 Positions of 0 in A289104; complement of A289106.

1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 19, 20, 22, 23, 26, 27, 29, 31, 32, 33, 34, 37, 38, 40, 42, 43, 44, 45, 48, 51, 52, 54, 55, 56, 58, 60, 61, 62, 63, 66, 69, 70, 72, 73, 74, 76, 78, 79, 80, 82, 83, 84, 85, 88, 89, 91, 92, 95, 98, 99, 101, 102, 103

Offset

1,2

Comments

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

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, A289105, A289106.

Sequence in context: A085007 A288992 A289017 * A289002 A039114 A188372

Adjacent sequences: A289102 A289103 A289104 * A289106 A289107 A289108

Keyword

nonn,easy

Author

Clark Kimberling, Jun 28 2017

Status

approved