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

1,3

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]}).

Links

Table of n, a(n) for n=1..132.

Formula

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

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 *)

Crossrefs

Cf. A191329, A191337, A191338, A191339.

Sequence in context: A093829 A113447 A137608 * A277349 A078807 A208249

Adjacent sequences: A191333 A191334 A191335 * A191337 A191338 A191339

Keyword

nonn

Author

Clark Kimberling, Jun 01 2011

Status

approved