OFFSET
1,2
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 1..18
Springer, Encyclopedia of Mathematics, Algebraic number
EXAMPLE
For n = 1 the minimal polynomial of 1 is z - 1 so a(1) = 1.
For n = 2 the minimal polynomial of 1 + sqrt(2) is z^2 - 2*z - 1 so a(2) = 2.
MAPLE
for n from 1 to 15 do
a:= convert(add(sqrt(i), i=1..n), RootOf);
P:= evala(Norm(a-z));
A[n]:= max(map(abs, [coeffs(P, z)]));
od:
seq(A[n], n=1..15); # Robert Israel, Sep 10 2014
MATHEMATICA
a[n_] := CoefficientList[ MinimalPolynomial[ Sqrt[Range[n]] // Total, x], x] // Abs // Max; Array[a, 12] (* Jean-François Alcover, Apr 29 2019 *)
PROG
(GAP) a:=function(n)
return MinimalPolynomial(Rationals, Sum([1..n], x->Sqrt(x)));
end; # Charles R Greathouse IV, Sep 12 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Sep 10 2014
STATUS
approved