login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I

%S 1,-3,2,-1,-2,2,-3,3,-6,4,-3,-4,12,-16,8,-6,5,-20,40,-40,16,-3,-3,15,

%T -40,60,-48,16,-9,7,-42,140,-280,336,-224,64,-9,-8,56,-224,560,-896,

%U 896,-512,128,-12,9,-72,336,-1008,2016,-2688,2304,-1152,256,-7,-5,45,-240

%N 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]]

%C Row sums are:

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

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

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

%e {1},

%e {-3, 2},

%e {-1, -2, 2},

%e {-3, 3, -6, 4},

%e {-3, -4, 12, -16, 8},

%e {-6, 5, -20, 40, -40, 16},

%e {-3, -3, 15, -40, 60, -48, 16},

%e {-9, 7, -42, 140, -280, 336, -224, 64},

%e {-9, -8, 56, -224, 560, -896, 896, -512, 128},

%e {-12, 9, -72, 336, -1008, 2016, -2688, 2304, -1152, 256},

%e {-7, -5, 45, -240, 840, -2016, 3360, -3840, 2880, -1280, 256}

%t << NumberTheory`AlgebraicNumberFields`

%t p[x_, n_] := If[n == 0, 1, MinimalPolynomial[(1 + Prime[n]^(1/n))/2, x]];

%t Table[CoefficientList[p[x, n], x], {n, 0, 10}];

%t Flatten[%]

%K sign,tabl,uned

%O 0,2

%A _Roger L. Bagula_, Mar 22 2010

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)