A257592 Number of zeros of the polynomial Sum_{j=0..n-1} z^(2^j-1)inside the unit circle.

1, 3, 5, 7, 17, 27, 51, 91, 183, 309, 617, 1125, 2097, 3995

Offset

3,2

Links

Table of n, a(n) for n=3..16.

Karl Dilcher and Larry Ericksen, The Polynomials of Mahler and Roots of Unity, The American Mathematical Monthly, Vol. 122, No. 04 (April 2015), pp. 338-353.

Mathematica

Table[Length[Select[Flatten[Abs[z/.NSolve[Sum[z^(2^j-1), {j, 0, n-1}]==0]]], #<1&]], {n, 3, 12}] (* Vaclav Kotesovec, May 17 2015, but for bigger n needs much memory (for n=14, 5 GB RAM) *)

Crossrefs

Cf. A257593.

Sequence in context: A086086 A141772 A220454 * A032496 A002092 A274906

Adjacent sequences: A257589 A257590 A257591 * A257593 A257594 A257595

Keyword

nonn,more

Author

N. J. A. Sloane, May 15 2015

Status

approved