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 A322796 a(n) = Kronecker symbol (n/6). 3
 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, 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, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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]. Also a(n) = Kronecker symbol (6/n) or (n/24) or (24/n). 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 {(-24/n)}, 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. LINKS Eric Weisstein's World of Mathematics, Kronecker Symbol (contains this sequence) Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,-1). FORMULA 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. Completely multiplicative with a(p) = a(p mod 24) for primes p. a(n) = A091337(n)*A102283(n). a(n) = A109017(n+12) = A109017(n-12). a(n) = a(-n) = a(n+24) for all n in Z. MATHEMATICA Array[KroneckerSymbol[6, #] &, 105, 0] (* Michael De Vlieger, Dec 31 2018 *) Table[KroneckerSymbol[6, n], {n, 0, 100}] (* Vincenzo Librandi, Jan 01 2019 *) PROG (PARI) a(n) = kronecker(n, 6) (MAGMA) [KroneckerSymbol(6, n): n in [0..100]]; // Vincenzo Librandi, Jan 01 2019 CROSSREFS Cf. A035188 (inverse Moebius transform). 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). Sequence in context: A285949 A285530 A317542 * A109017 A110161 A134667 Adjacent sequences:  A322793 A322794 A322795 * A322797 A322798 A322799 KEYWORD sign,easy,mult AUTHOR Jianing Song, Dec 26 2018 STATUS approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)