A190201 - OEIS

%I #9 Sep 08 2022 08:45:56

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

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

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

%N a(n) = [n*u+n*v]-[n*u]-[n*v], where u=sqrt(5), v=1/u, and []=floor.

%H G. C. Greubel, <a href="/A190201/b190201.txt">Table of n, a(n) for n = 1..10000</a>

%t u = 5^(1/2); v = 1/u;

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

%t t = Table[f[n], {n, 1, 120}] (*A190201*)

%t Flatten[Position[t, 0]]      (*A190202*)

%t Flatten[Position[t, 1]]      (*A190203*)

%o (PARI) for(n=1,30, print1(floor(n*(sqrt(5) + 1/sqrt(5))) - floor(n*sqrt(5)) - floor(n/sqrt(5)), ", ")) \\ _G. C. Greubel_, Dec 27 2017

%o (Magma) [Floor(n*(Sqrt(5) + 1/Sqrt(5))) - Floor(n*Sqrt(5)) - Floor(n/Sqrt(5)): n in [1..30]]; // _G. C. Greubel_, Dec 27 2017

%Y Cf. A190202, A190203.

%K nonn

%O 1

%A _Clark Kimberling_, May 05 2011