A011587 Legendre symbol (n,29).

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

Offset

0,1

Comments

The Dirichlet character associated with the real quadratic field Q(sqrt(29)). - 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,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1).

Formula

a(n) = (Product_{k=1..14} sin(2*k*Pi/29))/(Product_{k=1..14} sin(2*Pi/29)) = (sqrt(29)/2^14) * (Product_{k=1..14} sin(2*k*Pi/29)). - Jianing Song, Dec 13 2025

Completely multiplicative with a(29) = 0, a(p) = 1 if p^14 mod 29 = 1, and a(p) = -1 if p^14 mod 29 = 28. - Amiram Eldar, May 23 2026

Mathematica

JacobiSymbol[Range[0, 100], 29] (* Paolo Xausa, Nov 08 2025 *)

Crossrefs

Moebius transform of A035211.

Cf. A038901 (primes not inert in Q(sqrt(29))), A191022 (primes decomposing), A038902 (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, A011584, A322829, A322796, A390615, this sequence, A391502, A011589, A391503, A011590.

Sequence in context: A267084 A354807 A011586 * A011588 A011589 A011590

Adjacent sequences: A011584 A011585 A011586 * A011588 A011589 A011590

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved