A191340 - OEIS

%I #7 Aug 11 2016 05:48:28

%S 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,

%T 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,

%U 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

%N (A022839 mod 2)+(A108598 mod 2)

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

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

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

%H Ivan Neretin, <a href="/A191340/b191340.txt">Table of n, a(n) for n = 1..10000</a>

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

%t r = Sqrt[5]; s = r/(r - 1); h = 120;

%t u = Table[Floor[n*r], {n, 1, h}] (* A022839 *)

%t v = Table[Floor[n*s], {n, 1, h}] (* A108598 *)

%t w = Mod[u, 2] + Mod[v, 2] (* A191340 *)

%t Flatten[Position[w, 0]]  (* A191380 *)

%t Flatten[Position[w, 1]]  (* A191381 *)

%t Flatten[Position[w, 2]]  (* A191382 *)

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

%K nonn

%O 1,5

%A _Clark Kimberling_, Jun 01 2011