A011590 Legendre symbol (n,41).

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, -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, -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(41)). - 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

Paolo Xausa, 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,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1).

Formula

a(n) = (Prod_{1<=k<=20} sin(2*k*Pi/41))/(Prod_{1<=k<=20} sin(2*Pi/41)) = (sqrt(41)/2^20) * (Prod_{1<=k<=20} sin(2*k*Pi/41)). - Jianing Song, Dec 13 2025

Mathematica

JacobiSymbol[Range[0, 100], 41] (* Paolo Xausa, Nov 08 2025 *)

Crossrefs

Moebius transform of A035223.

Cf. A038919 (primes not inert in Q(sqrt(41))), A191030 (primes decomposing), A038920 (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, A011587, A391502, A011589, A391503, this sequence.

Sequence in context: A011587 A011588 A011589 * A011591 A011592 A011593

Adjacent sequences: A011587 A011588 A011589 * A011591 A011592 A011593

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved