A391503 - OEIS

A391503

a(n) = Kronecker symbol (10/n).

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

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OFFSET

COMMENTS

Also a(n) = (40/n).

The Dirichlet character associated with the real quadratic field Q(sqrt(10)) (discriminant 40).

LINKS

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

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

FORMULA

a(n) = A080891(n) * A091337(n).

Completely multiplicative with a(2) = a(5) = 0, a(p) = 1 for primes p == 1, 3, 9, 13, 27, 31, 37, 39 (mod 40), a(p) = -1 for primes p == 7, 11, 17, 19, 21, 23, 29, 33 (mod 40).

MATHEMATICA

a[n_] := KroneckerSymbol[10, n]; Array[a, 101, 0] (* Amiram Eldar, Mar 25 2026 *)

PROG

(PARI) a(n) = kronecker(10, n)

CROSSREFS

Moebius transform of A035192.

Cf. A038879 (primes not inert in Q(sqrt(10))), A097955 (primes decomposing), A038880 (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, this sequence, A011590.

Sequence in context: A289741 A185276 A388072 * A127266 A083923 A352824

Adjacent sequences: A391500 A391501 A391502 * A391504 A391505 A391506

KEYWORD

sign,easy,mult

AUTHOR

Jianing Song, Dec 11 2025

STATUS

approved