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A055035 Degree of minimal polynomial of sin(pi/n) over the rationals. 6
1, 1, 2, 2, 4, 1, 6, 4, 6, 2, 10, 4, 12, 3, 8, 8, 16, 3, 18, 8, 12, 5, 22, 8, 20, 6, 18, 12, 28, 4, 30, 16, 20, 8, 24, 12, 36, 9, 24, 16, 40, 6, 42, 20, 24, 11, 46, 16, 42, 10, 32, 24, 52, 9, 40, 24, 36, 14, 58, 16, 60, 15, 36, 32, 48, 10, 66, 32, 44, 12, 70, 24, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also degree of minimal polynomial of function F(n)=(gamma(1/n)*gamma((n-1)/n))/pi over the rationals. Roots of minimal polynomials of F(n) belonging to algebraic extension of sin(n/Pi) and vice versa (e.g. gamma(1/11)*gamma(10/11)/pi = 20*sin(pi/11) - 112*sin(pi/11)^3 + 256*sin(pi/11)^5 - 256*sin(pi/11)^7 + (1024*sin(pi/11)^9)/11). - Artur Jasinski, Oct 17 2011

The algebraic numbers sin(pi/(2*l)) are given in A228783 in the power basis of the number field Q(2*cos(pi/(2*l))) if n is even and of Q(2*cos(pi/l)) if l is odd. In A228785 sin(pi/(2*l+1)) is given in the power basis of Q(2*cos(pi/(2*(2*l+1)))) (only odd powers appear). The minimal polynomials for sin(pi/n), n>=1, are given in A228786. - Wolfdieter Lang, Oct 10 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..175

Eric Weisstein's World of Mathematics, Trigonometry Angles

FORMULA

a(1)=1, a(2)=1, a(n)=phi(n)/(1, 1, 2, 1 for n=0, 1, 2, 3 mod 4) for n>2, where phi is Euler's totient, A000010.

MATHEMATICA

a[n_] := If[n==2, 1, EulerPhi[n]/{1, 1, 2, 1}[[Mod[n, 4]+1]]]; Table[a[n], {n, 80}]

f[n_] := Exponent[ MinimalPolynomial[ Sin[ Pi/n]][x], x]; Array[f, 75] (* Robert G. Wilson v, Jul 28 2014 *)

CROSSREFS

Cf. A000010, A228786 (row length).

Sequence in context: A299020 A070306 A014665 * A235138 A204595 A173897

Adjacent sequences:  A055032 A055033 A055034 * A055036 A055037 A055038

KEYWORD

nonn,easy

AUTHOR

Shawn Cokus (Cokus(AT)math.washington.edu)

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)