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A257593 Number of zeros of the polynomial Sum_{j=0..n-1} z^(2^j-1)outside the unit circle. 1

%I #12 Sep 30 2017 02:34:29

%S 2,4,10,18,46,100,204,420,840,1708,3478,7066,14286,28772

%N Number of zeros of the polynomial Sum_{j=0..n-1} z^(2^j-1)outside the unit circle.

%H Karl Dilcher and Larry Ericksen, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.122.04.338">The Polynomials of Mahler and Roots of Unity</a>, The American Mathematical Monthly, Vol. 122, No. 04 (April 2015), pp. 338-353.

%t Table[Length[Select[Flatten[Abs[z/.NSolve[Sum[z^(2^j-1), {j, 0, n-1}]==0]]], #>1&]], {n, 3, 13}] (* _Vincenzo Librandi_, Sep 30 2017 *)

%Y Cf. A257592.

%K nonn,more

%O 3,1

%A _N. J. A. Sloane_, May 15 2015

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)