A189094 Zero-one sequence based on floor(sqrt(6)): a(A022840(k))=a(k); a(A138235(k))=1-a(k); a(1)=0.

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

Offset

1

Links

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

Example

Let u=A022840=(Beatty sequence for sqrt(6)) and v=A138235=(complement of u).  Then A189094 is the sequence a given by a(1)=0 and a(u(k))=a(k); a(v(k))=1-a(k).

Mathematica

r=6^(1/2); u[n_] := Floor[n*r];  (*A022840*)
a[1] = 0; h = 128;
c = (u[#1] &) /@ Range[2h];
d = (Complement[Range[Max[#1]], #1] &)[c]; (*A138235*)
Table[a[d[[n]]] = 1 - a[n], {n, 1, h - 1}]; (*A189094*)
Table[a[c[[n]]] = a[n], {n, 1, h}]   (*A189094*)
Flatten[Position[%, 0]]  (*A189095*)
Flatten[Position[%%, 1]] (*A189096*)

Crossrefs

A188967, A189095, A189096.

Sequence in context: A262808 A217206 A189097 * A041004 A141736 A190188

Adjacent sequences: A189091 A189092 A189093 * A189095 A189096 A189097

Keyword

nonn

Author

Clark Kimberling, Apr 16 2011

Status

approved