

A217290


Integers n such that 2*cos(2*Pi/n) is an integer.


6




OFFSET

0,1


COMMENTS

Terms are the allowable nfold 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



