proposed

approved

editing

proposed

allocatedPositions of 0 in forA289104; complement Clarkof KimberlingA289106.

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

1,2

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

Clark Kimberling, <a href="/A289105/b289105.txt">Table of n, a(n) for n = 1..10000</a>

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 *)

Cf. A001622, A289105, A289106.

allocated

nonn,easy

Clark Kimberling, Jun 28 2017

approved

editing

allocated for Clark Kimberling

allocated

approved