A011583 - OEIS

%I #23 Oct 21 2022 22:00:46

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

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

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

%N Legendre symbol (n,13).

%C Since 13 is an odd prime, this is the same as the Jacobi symbol (n,13). - _Robert Israel_, Jun 29 2017

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 68.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1).

%F G.f.: (x+x^3+2*x^4+x^5-x^7-2*x^8-x^9-x^11) / (1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12). - _Robert Israel_, Jun 29 2017

%p seq(numtheory:-legendre(n,13),n=0..80); # _Robert Israel_, Jun 29 2017

%t Table[JacobiSymbol[n, 13], {n, 0, 80}] (* _Jean-François Alcover_, May 17 2017 *)

%o (PARI) A011583(n) = kronecker(n,13) ;

%o for(n=0,20,print1(A011583(n)",") ); /* _R. J. Mathar_, Feb 25 2012 */

%K sign,mult,easy

%O 0,1

%A _N. J. A. Sloane_.