A190224 - OEIS

%I #12 Sep 08 2022 08:45:56

%S 1,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,

%T 0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,

%U 1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0

%N a(n) = [n*u + n*v] - [n*u] - [n*v], where u=sin(Pi/3), v=cos(Pi/3), and []=floor.

%H G. C. Greubel, <a href="/A190224/b190224.txt">Table of n, a(n) for n = 1..10000</a>

%t u = Sin[Pi/3]; v = Cos[Pi/3];

%t f[n_] := Floor[n*u + n*v] - Floor[n*u] - Floor[n*v]

%t t = Table[f[n], {n, 1, 120}] (* A190224 *)

%t Flatten[Position[t, 0]]      (* A190225 *)

%t Flatten[Position[t, 1]]      (* A190226 *)

%o (PARI) for(n=1,30, print1(floor(n*(sin(Pi/3) + cos(Pi/3))) - floor(n*cos(Pi/3)) - floor(n*sin(Pi/3)), ", ")) \\ _G. C. Greubel_, Dec 27 2017

%o (Magma) C<i> := ComplexField(); [Floor(n*Sin(Pi(C)/3) + n*Cos(Pi(C)/3)) - Floor(n*Sin(Pi(C)/3)) - Floor(n*Cos(Pi(C)/3)): n in [1..30]]; // _G. C. Greubel_, Dec 27 2017

%Y Cf. A180225, A180226.

%K nonn

%O 1

%A _Clark Kimberling_, May 06 2011