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A217290
Integers n such that 2*cos(2*Pi/n) is an integer.
3
-6, -4, -3, -2, -1, 1, 2, 3, 4, 6
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
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: A011408 A350094 A197760 * A157296 A329081 A343461
KEYWORD
sign,fini,full
AUTHOR
Raphie Frank, Sep 30 2012
STATUS
approved