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 A232209 Height of algebraic number 1 + sqrt(2) + ... + sqrt(n). 1
 1, 2, 16, 48, 10140, 6552, 721125376, 3620732928, 278799279816, 29925033224, 229926056690973293936640, 892398340719534485274624, 603207249820766251389767637583758341569376980491272, 240171846906336440253785749946778562802349467993472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let p(z) be the monic minimal polynomial of sum(j=1..n, sqrt(j)) over the integers. a(n) is the maximum of the absolute values of the coefficients of p(z). The degree of p(z) is at most A048656(n). Is it always equal to A048656(n)? 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 Cf. A048656. Sequence in context: A159010 A223219 A063721 * A012180 A058376 A295906 Adjacent sequences: A232206 A232207 A232208 * A232210 A232211 A232212 KEYWORD nonn AUTHOR Robert Israel, Sep 10 2014 STATUS approved

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Last modified February 9 04:43 EST 2023. Contains 360153 sequences. (Running on oeis4.)