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
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
KEYWORD
nonn,easy
AUTHOR
Rick L. Shepherd, Apr 23 2017
STATUS
approved