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A189480
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[4rn]-4[rn], where r=sqrt(5) and [ ]=floor.
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7
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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
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1,3
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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*)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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