A015582 - OEIS

%I #39 Oct 06 2019 03:05:15

%S 1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,

%T 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,

%U 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1

%N Inverse of 1573rd cyclotomic polynomial.

%C Periodic with period length 1573. - _Ray Chandler_, Apr 07 2017

%H Ray Chandler, <a href="/A015582/b015582.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_1320">Index entries for linear recurrences with constant coefficients</a>, order 1320.

%H <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>

%F cyclotomic(1573,x) is a polynomial of 120th order in the variable x^11, so it is c = 1 - x^11 - x^132 + x^264 + ... + x^1320, or with y = x^11 we can write c = 1 - y + y^11 - y^12 + y^13 - y^14 ... + y^120. - _R. J. Mathar_, Oct 20 2008

%p with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n, x), x,80); c(1573);

%t CoefficientList[Series[1/Cyclotomic[1573, x], {x, 0, 100}], x][[;; 81]] (* _Jean-François Alcover_, Jul 05 2011 *)

%Y Different from A014856 and A100910.

%K sign

%O 0,1

%A _Simon Plouffe_

%E Incorrect formula deleted by _N. J. A. Sloane_, Oct 20 2008