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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
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
Sequence in context: A308880 A319047 A276335 * A010873 A049804 A277904
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 23 2011
STATUS
approved

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Last modified July 17 18:09 EDT 2024. Contains 374377 sequences. (Running on oeis4.)