A285660 Degree of the algebraic number sin(n degrees) = sin(n Pi/180 radians).

1, 48, 12, 16, 24, 12, 4, 48, 24, 8, 3, 48, 8, 48, 12, 4, 24, 48, 2, 48, 6, 16, 12, 48, 8, 12, 12, 8, 24, 48, 1, 48, 24, 16, 12, 12, 4, 48, 12, 16, 6, 48, 4, 48, 24, 2, 12, 48, 8, 48, 3, 16, 24, 48, 2, 12, 24, 16, 12, 48, 2, 48, 12, 8, 24, 12, 4, 48, 24, 16, 3, 48, 4, 48, 12, 4, 24, 48, 4, 48, 6, 8, 12, 48, 8, 12, 12, 16, 24, 48, 1

Offset

0,2

Comments

By definition, a(n) is the degree of the minimal polynomial of sin(n degrees).

Periodic sequence of period 360.

The sequence range is the set of all divisors of 48 (A018261), where 48 = Euler_phi(180) = A000010(180).

All 48 distinct algebraic numbers of degree 48 referenced here (i.e., where GCD(n, 180) = 1) have the same minimal polynomial, which is shown in A019810.

Links

Table of n, a(n) for n=0..90.

Index entries for linear recurrences with constant coefficients, order 180.

Formula

a(n) = a(n-360) for all n (extending the sequence to negative n).

Example

sin(6 degrees) has minimal polynomial 16x^4 + 8x^3 - 16x^2 - 8x + 1 of degree 4, so a(6) = 4. sin(15 degrees) also has a minimal polynomial of degree 4 (but a different one, 16x^4 - 16x^2 + 1), so a(15) = 4.

Crossrefs

Cf. A019810 (sin(1 degree)), A018261 (divisors of 48), A007775.

Sequence in context: A298619 A298831 A087407 * A299585 A203250 A124354

Adjacent sequences: A285657 A285658 A285659 * A285661 A285662 A285663

Keyword

nonn,easy

Author

Rick L. Shepherd, Apr 23 2017

Status

approved