A189084 Zero-one sequence based on floor(sqrt(3)): a(A022838(k))=a(k); a(A054406(k))=1-a(k); a(1)=0.

0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1

Links

Table of n, a(n) for n=1..135.

Example

Let u=A022838=(Beatty sequence for sqrt(3)) and v=A054406=(complement of u).  Then A189084 is the sequence a given by a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

Mathematica

r=3^(1/2); u[n_] := Floor[n*r];  (*A022838*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[2h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A054406*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189084*)
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189084*)
Flatten[Position[%, 0]]  (*A189085*)
Flatten[Position[%%, 1]] (*A189086*)

Crossrefs

Cf. A188967, A189085, A189086.

Sequence in context: A215581 A156595 A286493 * A143222 A286490 A372728

Adjacent sequences: A189081 A189082 A189083 * A189085 A189086 A189087

Keyword

nonn

Author

Clark Kimberling, Apr 16 2011

Status

approved