A289036 Positions of 0 in A289035; complement of A289037.

1, 2, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93

Offset: 1

Author

Clark Kimberling, Jun 27 2017

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A289035, A289037.

Programs

Mathematica

z = 10; (* number of iterates *)
s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "010"}]
TableForm[Table[w[n], {n, 0, 10}]]
st = ToCharacterCode[w[z]] - 48   (* A289035 *)
Flatten[Position[st, 0]]  (* A289036 *)
Flatten[Position[st, 1]]  (* A289037 *)