A190886 - OEIS

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

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OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..132.

FORMULA

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

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 *)