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A174547
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Coefficients of minimal polynomials with roots a(n)=(1 + Prime[n+1]^(1/n))/2: p(x,n)=If[n == 0, 1, MinimalPolynomial[(1 + Prime[n+1]^(1/n))/2, x]]
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0
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1, -2, 1, -1, -1, 1, -4, 3, -6, 4, -5, -4, 12, -16, 8, -7, 5, -20, 40, -40, 16, -4, -3, 15, -40, 60, -48, 16, -10, 7, -42, 140, -280, 336, -224, 64, -11, -8, 56, -224, 560, -896, 896, -512, 128, -15, 9, -72, 336, -1008, 2016, -2688, 2304, -1152, 256, -15, -10, 90
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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, -3, -5, -6, -4, -9, -11, -14, -15,...}
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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]^(1/n))/2, x]];
t(n,m)=Coefficients(p(x,n))
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EXAMPLE
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{1},
{-2, 1},
{-1, -1, 1},
{-4, 3, -6, 4},
{-5, -4, 12, -16, 8},
{-7, 5, -20, 40, -40, 16},
{-4, -3, 15, -40, 60, -48, 16},
{-10, 7, -42, 140, -280, 336, -224, 64},
{-11, -8, 56, -224, 560, -896, 896, -512, 128},
{-15, 9, -72, 336, -1008, 2016, -2688, 2304, -1152, 256},
{-15, -10, 90, -480, 1680, -4032, 6720, -7680, 5760, -2560, 512}
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MATHEMATICA
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<< NumberTheory`AlgebraicNumberFields`
p[x_, n_] := If[n == 0, 1, MinimalPolynomial[(1 + Prime[n + 1]^(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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