A232627 Discriminants of the minimal polynomials of 2*sin(2*Pi/n) for n >= 1.

1, 1, 12, 1, 2000, 12, 1075648, 8, 1259712, 2000, 2414538435584, 1, 7340688973975552, 1075648, 324000000, 2048, 187591757103747287810048, 1259712, 1436650532447139184230793216, 5, 843466573910016, 2414538435584

Offset

1,3

Comments

The coefficient list for the minimal polynomials of 2*sin(2*Pi/n), called here MP(1; n, x), is given as A231188.

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Polynomial Discriminant.

Eric Weisstein's World of Mathematics, Vandermonde Determinant.

Formula

a(n) = discriminant of MP(1; n, x) = sum(A231188(n,m)*x^m, m=0..deg(1; n)) with the degree deg(1; n) = A093819(n), n >= 1.

Example

n=5: MP(1; 5, x) =  5 - 5*x^2 + x^4 with the four zeros x[1] = +sqrt(2 + tau), x[2] = -sqrt(2 + tau), x[3] = +sqrt(3 - tau), x[4] = -sqrt(3 - tau), with the golden section tau := (1 + sqrt(5))/2. They produce the discriminant(MP(1; 5, x)) = (Det(Vandermonde(4,[x[1],x[2],x[3],x[4]]))^2 = (20*sqrt(5))^2 = 2000.

Crossrefs

Cf. A231188, A093819.

Sequence in context: A225750 A157780 A223514 * A222582 A260621 A264024

Adjacent sequences: A232624 A232625 A232626 * A232628 A232629 A232630

Keyword

nonn,easy

Author

Wolfdieter Lang, Dec 12 2013

Status

approved