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]].

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

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: A026584 A396348 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