A189480 - OEIS

A189480

[4rn]-4[rn], where r=sqrt(5) and [ ]=floor.

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

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OFFSET

1,3

COMMENTS

Suppose, in general, 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. These b+1 (or b) position sequences comprise a partition of the positive integers.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000

MATHEMATICA

r=Sqrt[5];

f[n_]:=Floor[4 n*r]-4*Floor[n*r];

t=Table[f[n], {n, 1, 320}] (*A189480*)

Flatten[Position[t, 0]] (*A190813*)

Flatten[Position[t, 1]] (*A190883*)

Flatten[Position[t, 2]] (*A190884*)

Flatten[Position[t, 3]] (*A190885*)

CROSSREFS

Cf. A190813, A190883, A190884, A190885.