A257592 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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