A011583 Legendre symbol (n,13).

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, -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, 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

Offset

0,1

Comments

Since 13 is an odd prime, this is the same as the Jacobi symbol (n,13). - Robert Israel, Jun 29 2017

References

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

Links

Table of n, a(n) for n=0..80.

Index entries for linear recurrences with constant coefficients, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1).

Formula

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

Maple

seq(numtheory:-legendre(n, 13), n=0..80); # Robert Israel, Jun 29 2017

Mathematica

Table[JacobiSymbol[n, 13], {n, 0, 80}] (* Jean-François Alcover, May 17 2017 *)

Prog

(PARI) A011583(n) = kronecker(n, 13) ;
for(n=0, 20, print1(A011583(n)", ") ); /* R. J. Mathar, Feb 25 2012 */

Crossrefs

Sequence in context: A011582 A145568 A168185 * A011584 A011585 A267084

Adjacent sequences: A011580 A011581 A011582 * A011584 A011585 A011586

Keyword

sign,mult,easy

Author

N. J. A. Sloane.

Status

approved