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A174543
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Coefficients of minimal polynomials with roots a(n)=(1 + Prime[n]^(1/n))/2: p(x,n)=If[n == 0, 1, MinimalPolynomial[(1 + Prime[n]^(1/n))/2, x]]
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0
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1, -3, 2, -1, -2, 2, -3, 3, -6, 4, -3, -4, 12, -16, 8, -6, 5, -20, 40, -40, 16, -3, -3, 15, -40, 60, -48, 16, -9, 7, -42, 140, -280, 336, -224, 64, -9, -8, 56, -224, 560, -896, 896, -512, 128, -12, 9, -72, 336, -1008, 2016, -2688, 2304, -1152, 256, -7, -5, 45, -240
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OFFSET
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0,2
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COMMENTS
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Row sums are:
{1, -1, -1, -2, -3, -5, -3, -8, -9, -11, -7}
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LINKS
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FORMULA
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p(x,n)=If[n == 0, 1, MinimalPolynomial[(1 + Prime[n]^(1/n))/2, x]];
t(n,m)=Coefficients(p(x,n))
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EXAMPLE
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{1},
{-3, 2},
{-1, -2, 2},
{-3, 3, -6, 4},
{-3, -4, 12, -16, 8},
{-6, 5, -20, 40, -40, 16},
{-3, -3, 15, -40, 60, -48, 16},
{-9, 7, -42, 140, -280, 336, -224, 64},
{-9, -8, 56, -224, 560, -896, 896, -512, 128},
{-12, 9, -72, 336, -1008, 2016, -2688, 2304, -1152, 256},
{-7, -5, 45, -240, 840, -2016, 3360, -3840, 2880, -1280, 256}
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MATHEMATICA
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<< NumberTheory`AlgebraicNumberFields`
p[x_, n_] := If[n == 0, 1, MinimalPolynomial[(1 + Prime[n]^(1/n))/2, x]];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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