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A020735
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Odd numbers >= 5.
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2
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5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Values of n such that a regular polygon with n sides can be formed by tying knots in a strip of paper. - Robert A. J. Matthews (rajm(AT)compuserve.com)
These polygons fill in many of the gaps left by the Greeks, who were restricted to compass and ruler. Specifically, they make possible construction of the regular 7-sided heptagon, 9-sided nonagon, 11-gon and 13-gon. The 14-gon becomes the first to be impossible by either ruler, compass or knotting.
Continued fraction expansion of 2/(exp(2)-7). - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Nov 04 2003
Pisot sequence T(5,7). - David W. Wilson (davidwwilson(AT)comcast.net)
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REFERENCES
| F. V. Morley, Proc. Lond. Math. Soc., Jun 1923
F. V. Morley, "Inversive Geometry" (George Bell, 1933; reprinted Chelsea Publishing Co. 1954)
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LINKS
| Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = 2*n + 3.
G.f.: x*(5-3*x)/(1-2*x+x^2). a(n) = 2*a(n-1)-a(n-2). - Colin Barker, Jan 31 2012
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CROSSREFS
| Subsequence of A005408. See A008776 for definitions of Pisot sequences.
Sequence in context: A084926 A049013 A062545 * A108144 A123910 A024886
Adjacent sequences: A020732 A020733 A020734 * A020736 A020737 A020738
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2007
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