A390615 - OEIS

%I #16 Mar 25 2026 15:55:14

%S 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,

%T 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,

%U 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

%N a(n) = Kronecker symbol (28/n).

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

%H Amiram Eldar, <a href="/A390615/b390615.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1,0,1,0,-1,0,1,0,-1).

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

%F 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).

%t a[n_] := KroneckerSymbol[28, n]; Array[a, 101, 0] (* _Amiram Eldar_, Mar 25 2026 *)

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

%Y Moebius transform of A035210.

%Y Cf. A038878 (primes not inert in Q(sqrt(7))), A296934 (primes decomposing), A003632 (prime remaining inert).

%Y 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.

%Y 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.

%K sign,easy,mult

%O 0

%A _Jianing Song_, Dec 11 2025