A011584 Legendre symbol (n,17).

0, 1, 1, -1, 1, -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, 1, -1, 1, 1, 0, 1, 1, -1, 1, -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, 1, -1, 1, 1, 0, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1

Offset

0,1

Comments

The Dirichlet character associated with the real quadratic field Q(sqrt(17)). - Jianing Song, Dec 13 2025

References

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

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = (Product_{k=1..8} sin(2*k*Pi/17))/(Product_{k=1..8} sin(2*Pi/17)) = (sqrt(17)/2^8) * (Product_{k=1..8} sin(2*k*Pi/17)). - Jianing Song, Dec 13 2025

Completely multiplicative with a(17) = 0, a(p) = 1 if p^8 mod 17 = 1, and a(p) = -1 if p^8 mod 17 = 16. - Amiram Eldar, May 23 2026

Mathematica

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

Prog

(PARI) A011584(n) = kronecker(n, 17) ;
for(n=0, 20, print1(A011584(n)", ") ); /* R. J. Mathar, Feb 25 2012 */

Crossrefs

Moebius transform of A035199.

Cf. A038889 (primes not inert in Q(sqrt(17))), A296938 (primes decomposing), A038890 (primes remaining inert).

Kronecker symbols {(D/n)} for negative fundamental discriminants D = -3..-47, -67, -163: A102283, A101455, A175629, A188510, A011582, A316569, A011585, A289741, A011586, A109017, A011588, A390614, A388073, A388072, A011591, A011592, A011596, A011615.

Kronecker symbols {(D/n)} for positive fundamental discriminants D = 5..41: A080891, A091337, A110161, A011583, this sequence, A322829, A322796, A390615, A011587, A391502, A011589, A391503, A011590.

Sequence in context: A145568 A168185 A011583 * A011585 A267084 A354807

Adjacent sequences: A011581 A011582 A011583 * A011585 A011586 A011587

Keyword

sign,easy,mult

Author

N. J. A. Sloane

Status

approved