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A285660
Degree of the algebraic number sin(n degrees) = sin(n Pi/180 radians).
0
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.
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
KEYWORD
nonn,easy
AUTHOR
Rick L. Shepherd, Apr 23 2017
STATUS
approved