A191340 (A022839 mod 2)+(A108598 mod 2)

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

Offset

1,5

Comments

Let r=sqrt(5) and s=r/(r-1). There numbers yield the following two complementary Beatty sequences:

A022839(n)=[nr], A108598(n)=[ns], where [ ]=floor.

A191340(n)=the number of odd numbers in {[nr], [ns]}.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n)=([nr] mod 2)+([ns] mod 2), where r=sqrt(5), s=r/(r-1), [ ]=floor.

Mathematica

r = Sqrt[5]; s = r/(r - 1); h = 120;
u = Table[Floor[n*r], {n, 1, h}] (* A022839 *)
v = Table[Floor[n*s], {n, 1, h}] (* A108598 *)
w = Mod[u, 2] + Mod[v, 2] (* A191340 *)
Flatten[Position[w, 0]]  (* A191380 *)
Flatten[Position[w, 1]]  (* A191381 *)
Flatten[Position[w, 2]]  (* A191382 *)

Crossrefs

Cf. A191329, A191336, A191380, A191381, A191382.

Sequence in context: A337586 A345006 A086831 * A211229 A335621 A316675

Adjacent sequences: A191337 A191338 A191339 * A191341 A191342 A191343

Keyword

nonn

Author

Clark Kimberling, Jun 01 2011

Status

approved