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A217290
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Integers n such that 2*cos(2*Pi/n) is an integer.
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3
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OFFSET
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0,1
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COMMENTS
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Terms are the allowable n-fold rotational symmetries of a crystal (rotation by 360 degrees/n leaves the object unchanged).
The positive values of this sequence {1, 2, 3, 4, 6} are the proper divisors of 12, all having a totient of 1 or 2 (see A000010).
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LINKS
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Table of n, a(n) for n=0..9.
W. Scherrer, Die Einlagerung eines regulären Vielecks in ein Gitter, Elemente der Mathematik, 1946, 1(6), p.97-98.
Wikipedia, Crystallographic Restriction Theorem
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EXAMPLE
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2*cos(2Pi/1) = 2
2*cos(2Pi/2) = -2
2*cos(2Pi/3) = -1
2*cos(2Pi/4) = 0
2*cos(2Pi/6) = 1
2*cos(2Pi/10) = 1.6180339887... and so 10, for instance, is not in this sequence.
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CROSSREFS
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Sequence in context: A011408 A350094 A197760 * A157296 A329081 A343461
Adjacent sequences: A217287 A217288 A217289 * A217291 A217292 A217293
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KEYWORD
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sign,fini,full
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AUTHOR
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Raphie Frank, Sep 30 2012
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STATUS
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approved
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