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A189480 [4rn]-4[rn], where r=sqrt(5) and [ ]=floor. 7
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 (list; graph; refs; listen; history; text; internal format)
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.

Sequence in context: A308880 A319047 A276335 * A010873 A049804 A277904

Adjacent sequences:  A189477 A189478 A189479 * A189481 A189482 A189483

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 23 2011

STATUS

approved

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Last modified October 21 17:37 EDT 2021. Contains 348155 sequences. (Running on oeis4.)