A390615 a(n) = Kronecker symbol (28/n).

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

Offset

0

Comments

The Dirichlet character associated with the real quadratic field Q(sqrt(7)) (discriminant 28).

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,0,1,0,-1,0,1,0,-1).

Formula

a(n) = A101455(n) * A175629(n).

Completely multiplicative with a(2) = a(7) = 0, a(p) = 1 for primes p == 1, 3, 9, 19, 25, 27 (mod 28), a(p) = -1 for primes p == 5, 11, 13, 15, 17, 23 (mod 28).

Mathematica

a[n_] := KroneckerSymbol[28, n]; Array[a, 101, 0] (* Amiram Eldar, Mar 25 2026 *)

Prog

(PARI) a(n) = kronecker(28, n)

Crossrefs

Moebius transform of A035210.

Cf. A038878 (primes not inert in Q(sqrt(7))), A296934 (primes decomposing), A003632 (prime 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, this sequence, A011587, A391502, A011589, A391503, A011590.

Sequence in context: A358670 A379971 A288524 * A112416 A061265 A288466

Adjacent sequences: A390612 A390613 A390614 * A390616 A390617 A390618

Keyword

sign,easy,mult

Author

Jianing Song, Dec 11 2025

Status

approved