A190886 a(n) = [5nr]-5[nr], where r=sqrt(5).

1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0

Offset: 1

Author

Clark Kimberling, May 26 2011

Keywords

• nonn

Comments

In general, suppose that a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. For c=0, there are b of these position sequences, and they comprise a partition of the positive integers.

Crossrefs

Cf. A190887, A190888, A190889, A190890, A190891.

Programs

Mathematica

r = Sqrt[5];
f[n_] := Floor[5n*r] - 5*Floor[n*r]
t = Table[f[n], {n, 1, 400}] (* A190886 *)
Flatten[Position[t, 0]]      (* A190887 *)
Flatten[Position[t, 1]]      (* A190888 *)
Flatten[Position[t, 2]]      (* A190889 *)
Flatten[Position[t, 3]]      (* A190890 *)
Flatten[Position[t, 4]]      (* A190891 *)

Formula

a(n) = [5nr]-5[nr], where r=sqrt(5).