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A332420
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Number of Maclaurin polynomials of sin x having exactly n positive zeros.
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1
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3, 4, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 4, 5
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OFFSET
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1,1
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COMMENTS
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a(1) counts these values of 2n-1: 3, 5, and 11. The single zeros of p(3,x), p(5,x), and p(11,x) are sqrt(6), 3.078642..., and 3.141148..., respectively.
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LINKS
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MATHEMATICA
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z = 60; p[n_, x_] := Normal[Series[Sin[x], {x, 0, n}]];
t[n_] := x /. NSolve[p[n, x] == 0, x, z];
u[n_] := Select[t[n], Im[#] == 0 && # > 0 &];
v = Table[Length[u[n]], {n, 2, 30}]
(1/2) Table[Count[v, n], {n, 1, 40}]
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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