A113402 -id:A113402 - cp's OEIS frontend

A089929 Algebraic degree of cot(Pi/n).

1, 2, 1, 4, 2, 6, 2, 6, 4, 10, 2, 12, 6, 8, 4, 16, 6, 18, 4, 12, 10, 22, 4, 20, 12, 18, 6, 28, 8, 30, 8, 20, 16, 24, 6, 36, 18, 24, 8, 40, 12, 42, 10, 24, 22, 46, 8, 42, 20, 32, 12, 52, 18, 40, 12, 36, 28, 58, 8, 60, 30, 36, 16, 48, 20, 66, 16, 44, 24, 70, 12

Offset: 2

Eric W. Weisstein, Nov 15 2003

Also the algebraic degrees of the surface area and volume of an n-prism with unit edge lengths.

Jon Maiga, Table of n, a(n) for n = 1...400
Eric Weisstein's World of Mathematics, Prism
Eric Weisstein's World of Mathematics, Regular Polygon
Eric Weisstein's World of Mathematics, Cotangent

Cf. A055035, A113402.

a[n_] := Exponent[ MinimalPolynomial[ Cot[Pi/n]][x], x]; Table[ a[n], {n, 2, 52}] (* Jean-François Alcover, Oct 03 2012 *)

a(n) = A000010(n/gcd(n, 2)) (conjectured). - Jon Maiga, Sep 01 2019

a(47) corrected and more terms added by Jon Maiga, Sep 01 2019

A113401 Algebraic degree of cos(2*Pi/n) for constructible n-gons (A003401).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 2, 2, 4, 4, 8, 4, 4, 4, 8, 8, 8, 8, 16, 8, 16, 16, 16, 32, 16, 16, 16, 32, 32, 32, 32, 32, 32, 32, 64, 64, 128, 64, 64, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 256, 128, 128, 128, 256, 256, 256, 256, 512, 256, 256, 256, 256, 256, 256, 512

Offset: 1

Eric W. Weisstein, Oct 28 2005

Eric Weisstein's World of Mathematics, Trigonometry Angles

Cf. A003401, A023022, A113402.

cp's OEIS Frontend

A089929 Algebraic degree of cot(Pi/n).

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