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Search: id:A102302
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| A102302 |
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Largest number < n/2 coprime to n. The densest possible star-shaped regular n-gon is formed by connecting with straight lines every a(n)th point out of n regularly spaced points lying on a circumference. |
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+0
2
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| 3, 3, 4, 3, 5, 5, 6, 5, 7, 7, 8, 7, 9, 9, 10, 9, 11, 11, 12, 11, 13, 13, 14, 13, 15, 15, 16, 15, 17, 17, 18, 17, 19, 19, 20, 19, 21, 21, 22, 21, 23, 23, 24, 23, 25, 25, 26, 25, 27, 27, 28, 27, 29, 29, 30, 29, 31, 31, 32, 31, 33, 33, 34, 33, 35, 35, 36, 35, 37, 37, 38, 37, 39, 39
(list; graph; listen)
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OFFSET
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7,1
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COMMENT
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For a given n there are A055684(n) different star-shaped regular polygons. The minimum skip increment for connecting points on the circumference is given by A053669(n), the maximum skip increment is given by a(n). There are no star-shaped polygons for n=3,4,6 and unique star-shaped polygons for n=5,8,10 and 12, for which a(n)=A053669(n).
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LINKS
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Hugo Pfoertner, (Star-Shaped-) Polygons with Maximal Density.
Hugo Pfoertner, Star-shaped regular polygons.
Eric Weisstein's World of Mathematics, Star Polygon.
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FORMULA
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a(4*k-1)=a(4*k)=a(4*k+2)=2*k-1; a(4*k+1)=2*k
(1/2) [n - (I^n + (-I)^n)/2 - (-1)^n + 4 ]. - Ralf Stephan, May 17 2007
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CROSSREFS
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Cf. A053669 least number coprime to n, A055684 number of different n-pointed stars.
Sequence in context: A096139 A138372 A123708 this_sequence A130896 A029882 A163523
Adjacent sequences: A102299 A102300 A102301 this_sequence A102303 A102304 A102305
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KEYWORD
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easy,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 23 2005
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