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

Author

Rick L. Shepherd, Apr 23 2017

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

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

Formula

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