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Search: id:A036415
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| A036415 |
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Values of n for which there are no empty intervals when fractional part(m*GoldenRatio) for m = 1, ..., n is plotted along [ 0, 1 ] subdivided into n equal regions. |
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+0
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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sequence contains the Fibonacci numbers A000045.
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REFERENCES
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Steinhaus, H., Mathematical Snapshots, 3rd American ed., New York: Oxford University Press, pp. 48-49, 1983.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Golden Ratio
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MATHEMATICA
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phi = (Sqrt[5] - 1)/2; a = {}; m = {}; Do[AppendTo[a, N[n*phi - Floor[n*phi], 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
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Cf. A036414.
Sequence in context: A054961 A141283 A080078 this_sequence A086736 A017846 A129976
Adjacent sequences: A036412 A036413 A036414 this_sequence A036416 A036417 A036418
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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No others with n<=28657.
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