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

Author

N. J. A. Sloane

Keywords

• sign
• mult
• easy

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

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

Programs

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 *)

PARI

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

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