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A036415
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Values of n for which there are no empty intervals when fractional part(m*phi) for m = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The sequence contains the Fibonacci numbers A000045.
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REFERENCES
| Steinhaus, H., Mathematical Snapshots, 3rd American ed., New York: Oxford University Press, pp. 48-49, 1983.
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LINKS
| Eric Weisstein's World of Mathematics, Equidistributed Sequence
Eric Weisstein's World of Mathematics, Golden Ratio
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MATHEMATICA
| a = {}; m = {}; Do[AppendTo[a, N[n*GoldenRatio - Floor[n*GoldenRatio], 50]]; a = Sort[a]; b = {0}; Do[AppendTo[b, k/n], {k, 1, n}]; b = Sort[b]; c = 0; Do[If[(a[[k]] < b[[k + 1]]) && (a[[k]] > b[[k]]), [null], c = 1], {k, 1, Length[a]}]; If[c == 0, AppendTo[m, n]], {n, 1, 1000}]; m - Artur Jasinski (grafix(AT)csl.pl), Dec 27 2007
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CROSSREFS
| Cf. A036414.
Sequence in context: A141283 A186445 A080078 * A086736 A175773 A017846
Adjacent sequences: A036412 A036413 A036414 * A036416 A036417 A036418
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| No others with n <= 28657.
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