A081797 Maximal coefficient (in absolute value) of the minimal polynomial P with integer coefficients such that P(sin(Pi/n)) = 0.

1, 1, 4, 2, 20, 2, 112, 8, 96, 4, 2816, 16, 16640, 8, 448, 256, 487424, 8, 2723840, 512, 11264, 32, 85917696, 512, 13107200, 80, 2236416, 13568, 15386804224, 16, 84515225600, 212992, 10911744, 448, 343670784, 13824, 15625695002624, 1024

Offset

1,3

Comments

It appears that when n > 3 is prime, n divides a(n). - T. D. Noe, Jan 06 2008

Links

Table of n, a(n) for n=1..38.

Example

x=sin(Pi/9) satisfies 64x^6 - 96x^4 + 36x^2 - 3 = 0, hence a(9)=96.

Mathematica

Table[Max[Abs[CoefficientList[MinimalPolynomial[Sin[Pi/n], x], x]]], {n, 20}] (* T. D. Noe, Jan 06 2008 *)

Crossrefs

Cf. A055034.

Sequence in context: A305135 A177248 A191706 * A354094 A347590 A016517

Adjacent sequences: A081794 A081795 A081796 * A081798 A081799 A081800

Keyword

nonn

Author

Benoit Cloitre, Apr 10 2003

Extensions

More terms from T. D. Noe, Jan 06 2008

Status

approved