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A174543 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]] 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:

{1, -1, -1, -2, -3, -5, -3, -8, -9, -11, -7}

LINKS

Table of n, a(n) for n=0..58.

FORMULA

p(x,n)=If[n == 0, 1, MinimalPolynomial[(1 + Prime[n]^(1/n))/2, x]];

t(n,m)=Coefficients(p(x,n))

EXAMPLE

{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}

MATHEMATICA

<< 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[%]

CROSSREFS

Sequence in context: A256794 A068929 A060567 * A260450 A036583 A047878

Adjacent sequences:  A174540 A174541 A174542 * A174544 A174545 A174546

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 22 2010

STATUS

approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)