A191336 (A022838 mod 2)+(A054406 mod 2).

1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 2, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 2, 1, 0

Offset: 1

Author

Clark Kimberling, Jun 01 2011

Keywords

• nonn

Comments

A022838: Beatty sequence for r=sqrt(3),

A054406: Beatty sequence for s=(3+sqrt(3))/2 (complement

of A022838), so that

A191336(n)=([nr] mod 2)+([ns] mod 2), where [ ]=floor.

A191336(n)=(number of odd numbers in {[nr],[ns]}).

Crossrefs

Cf. A191329, A191337, A191338, A191339.

Programs

Mathematica

r = Sqrt[3]; s = r/(r - 1); h = 320;
u = Table[Floor[n*r], {n, 1, h}] (* A022838 *)
v = Table[Floor[n*s], {n, 1, h}] (* A054406 *)
w = Mod[u, 2] + Mod[v, 2] (* A191336 *)
Flatten[Position[w, 0]]   (* A191337 *)
Flatten[Position[w, 1]]   (* A191338 *)
Flatten[Position[w, 2]]   (* A191339 *)

Formula

a(n)=([nr] mod 2)+([ns] mod 2), where r=sqrt(3), s=r/(r-1), and [ ]=floor.