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A215046 Increasingly ordered list of those values m for which the degree of the minimal polynomial of 2*cos(Pi/m) (see A187360) is prime. 0
4, 5, 6, 7, 9, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The degree delta(m) of the minimal polynomial of rho(m) := 2*cos(Pi/m), called C(m,x) with coefficient array A187360, is given by A055034(m).

If delta(m) = phi(2*m)/2, m>=2, delta(1) = 1, with phi = A000010, is prime then the (Abelian) Galois group G(Q(rho(m))/Q) is cyclic. Because this Galois group of C(m,x) has order delta(m) this follows from a corollary to Lagrange's theorem, or also from Cauchy's theorem on groups.

Because the mentioned Galois group is isomorphic to the multiplicative group Modd m of order delta(m) (see a comment on A203571) all m = a(n) values appear in A206551.

This sequence is also a subsequence of A210845 because p is squarefree (see A005117).

LINKS

Table of n, a(n) for n=1..47.

FORMULA

phi(2*m)/2 is prime iff m=a(n), n>=1, with phi = A000010 (Euler's totient).

EXAMPLE

a(4) = 7, because 7 satisfies phi(14)/2 = phi(2*7)/2 = 1*6/2 = 3, which is prime; and 7 is the fourth smallest number m satisfying: phi(2*m)/2 is prime.

CROSSREFS

Cf. A055034.

Sequence in context: A010381 A095033 A010399 * A008523 A047568 A139453

Adjacent sequences:  A215043 A215044 A215045 * A215047 A215048 A215049

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Sep 03 2012

STATUS

approved

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Last modified April 19 22:22 EDT 2019. Contains 322291 sequences. (Running on oeis4.)