This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322796 #28 Feb 16 2025 08:33:57
%S A322796 0,1,0,0,0,1,0,-1,0,0,0,-1,0,-1,0,0,0,-1,0,1,0,0,0,1,0,1,0,0,0,1,0,-1,
%T A322796 0,0,0,-1,0,-1,0,0,0,-1,0,1,0,0,0,1,0,1,0,0,0,1,0,-1,0,0,0,-1,0,-1,0,
%U A322796 0,0,-1,0,1,0,0,0,1,0,1,0,0,0,1,0,-1,0,0,0,-1,0
%N A322796 a(n) = Kronecker symbol (6/n).
%C A322796 Period 24: repeat [0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1].
%C A322796 Also a(n) = Kronecker symbol (24/n).
%C A322796 This sequence is one of the seven non-principal real Dirichlet characters modulo 24. The other six are Jacobi or Kronecker symbols {(-6/n)} (or {(n/6)}, {(-24/n)}, {(n/24)}, A109017), {(-12/n)} (or {(n/12)}, A134667), {(12/n)} (A110161), {(-18/n)} (or {(-72/n)}), {(18/n)} (or {(72/n)}, {(n/72)}) and {(-36/n)}. These sequences all become the same after taking absolute values.
%H A322796 Antti Karttunen, <a href="/A322796/b322796.txt">Table of n, a(n) for n = 0..65543</a>
%H A322796 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KroneckerSymbol.html">Kronecker Symbol</a> (contains this sequence)
%H A322796 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,0,0,-1).
%F A322796 a(n) = 1 for n == 1, 5, 19, 23 (mod 24); -1 for n == 7, 11, 13, 17 (mod 24); 0 for n that are not coprime with 21.
%F A322796 Completely multiplicative with a(p) = a(p mod 24) for primes p.
%F A322796 a(n) = A091337(n)*A102283(n).
%F A322796 a(n) = A109017(n+12) = A109017(n-12).
%F A322796 a(n) = a(-n) = a(n+24) for all n in Z.
%t A322796 Array[KroneckerSymbol[6, #] &, 105, 0] (* _Michael De Vlieger_, Dec 31 2018 *)
%t A322796 Table[KroneckerSymbol[6, n], {n, 0, 100}] (* _Vincenzo Librandi_, Jan 01 2019 *)
%o A322796 (PARI) a(n) = kronecker(6, n); \\ --- Argument order corrected by _Antti Karttunen_, Sep 27 2019
%o A322796 (Magma) [KroneckerSymbol(6, n): n in [0..100]]; // _Vincenzo Librandi_, Jan 01 2019
%Y A322796 Cf. A035188 (inverse Moebius transform).
%Y A322796 Kronecker symbols {(d/n)} where d is a fundamental discriminant with |d| <= 24: A109017 (d=-24), A011586 (d=-23), A289741 (d=-20), A011585 (d=-19), A316569 (d=-15), A011582 (d=-11), A188510 (d=-8), A175629 (d=-7), A101455 (d=-4), A102283 (d=-3), A080891 (d=5), A091337 (d=8), A110161 (d=12), A011583 (d=13), A011584 (d=17), A322829 (d=21), this sequence (d=24).
%K A322796 sign,easy,mult
%O A322796 0,1
%A A322796 _Jianing Song_, Dec 26 2018
%E A322796 Definition corrected by _Antti Karttunen_, Sep 28 2019