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A217290 Integers n such that 2*cos(2*Pi/n) is an integer. 6
-6, -4, -3, -2, -1, 1, 2, 3, 4, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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).

LINKS

Table of n, a(n) for n=0..9.

Wikipedia, Crystallographic Restriction Theorem

EXAMPLE

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.

CROSSREFS

Sequence in context: A093604 A011408 A197760 * A157296 A329081 A155044

Adjacent sequences:  A217287 A217288 A217289 * A217291 A217292 A217293

KEYWORD

sign,fini,full

AUTHOR

Raphie Frank, Sep 30 2012

STATUS

approved

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)