A190236 a(n) = [n*u + n*v] -[n*u] -[n*v], where u=1/2, v=(1+sqrt(5))/2, and []=floor.

1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1

Offset

1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

u = 1/2; v = GoldenRatio;
f[n_] := Floor[n*u + n*v] - Floor[n*u] - Floor[n*v]
t = Table[f[n], {n, 1, 120}] (* A190236 *)
Flatten[Position[t, 0]]      (* A190237 *)
Flatten[Position[t, 1]]      (* A190238 *)
Table[Floor[n*(2 + Sqrt[5])/2] - Floor[n/2] - Floor[n*(1 + Sqrt[5])/2], {n, 1, 50}] (* G. C. Greubel, Dec 27 2017 *)

Prog

(PARI) for(n=1, 30, print1(floor(n*(2 + sqrt(5))/2) - floor(n/2) - floor(n*(1 + sqrt(5))/2), ", ")) \\ G. C. Greubel, Dec 27 2017
(Magma) [Floor(n*(1+Sqrt(5))/2) - Floor(n/2) - Floor(n*(1+Sqrt(5))/2): n in [1..30]]; // G. C. Greubel, Dec 27 2017

Crossrefs

Cf. A190237, A190238.

Sequence in context: A225569 A087032 A236677 * A190224 A352678 A373371

Adjacent sequences: A190233 A190234 A190235 * A190237 A190238 A190239

Keyword

nonn

Author

Clark Kimberling, May 06 2011

Status

approved