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A174547 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]] 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:

{1, -1, -1, -3, -5, -6, -4, -9, -11, -14, -15,...}

LINKS

Table of n, a(n) for n=0..57.

FORMULA

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

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

EXAMPLE

{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}

MATHEMATICA

<< 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[%]

CROSSREFS

Sequence in context: A046876 A026584 A247342 * A119326 A219866 A333418

Adjacent sequences:  A174544 A174545 A174546 * A174548 A174549 A174550

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 22 2010

STATUS

approved

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Last modified July 31 22:03 EDT 2021. Contains 346377 sequences. (Running on oeis4.)