A391502 - OEIS

%I #13 Mar 25 2026 15:55:07

%S 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,

%T 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,

%U -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

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

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

%H Amiram Eldar, <a href="/A391502/b391502.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,1,0,-1,1,0,-1,1,-1,0,1,-1,0,1,-1,0,1,-1).

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

%F 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).

%t a[n_] := KroneckerSymbol[33, n]; Array[a, 101, 0] (* _Amiram Eldar_, Mar 25 2026 *)

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

%Y Moebius transform of A035215.

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

%K sign,easy,mult

%O 0

%A _Jianing Song_, Dec 11 2025