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A285660
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Degree of the algebraic number sin(n degrees) = sin(n Pi/180 radians).
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0
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = a(n-360) for all n (extending the sequence to negative n).
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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