A391502 - OEIS

A391502

a(n) = Kronecker symbol (33/n).

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

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OFFSET

COMMENTS

The Dirichlet character associated with the real quadratic field Q(sqrt(33)).

LINKS

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

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

FORMULA

a(n) = A102283(n) * A011582(n).

Completely multiplicative with a(3) = a(11) = 0, a(p) = 1 for primes p == 1, 2, 4, 8, 16, 17, 25, 29, 31, 32 (mod 33), a(p) = -1 for primes p == 5, 7, 10, 13, 14, 19, 20, 23, 26, 28 (mod 33).

MATHEMATICA

a[n_] := KroneckerSymbol[33, n]; Array[a, 101, 0] (* Amiram Eldar, Mar 25 2026 *)

PROG

(PARI) a(n) = kronecker(33, n)

CROSSREFS

Moebius transform of A035215.

Cf. A038907 (primes not inert in Q(sqrt(33))), A038908 (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, A390615, A011587, this sequence, A011589, A391503, A011590.

Sequence in context: A189479 A260394 A181932 * A284792 A094217 A388073

Adjacent sequences: A391499 A391500 A391501 * A391503 A391504 A391505

KEYWORD

sign,easy,mult

AUTHOR

Jianing Song, Dec 11 2025

STATUS

approved