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A036415
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Values of k for which there are no empty intervals when fractional part(m*phi) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.
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2
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1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040
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OFFSET
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1,2
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COMMENTS
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The sequence contains the Fibonacci numbers A000045.
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REFERENCES
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H. Steinhaus, Mathematical Snapshots, 3rd American ed., New York: Oxford University Press, pp. 48-49, 1983.
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LINKS
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MATHEMATICA
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With[{f = FractionalPart[GoldenRatio Range[1000]]}, Position[Table[Count[BinCounts[Take[f, n], {0., 1, 1/n}], 0], {n, Length[f]}], 0]] // Flatten (* Eric W. Weisstein, Apr 27 2024 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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