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A226162
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a(n) = Kronecker Symbol (-5/n), n >= 0.
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4
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0, 1, -1, 1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, -1, 0, 1, -1, -1, -1, 0, 1, 1, 1, -1, 0, 1, 1, 1, 1, 0, -1, -1, -1, 1, 0, 1, -1, 1, -1, 0, 1, -1, 1, -1, 0, -1, 1, 1, 1, 0, -1, -1, -1, -1, 0, -1, -1, -1, -1, 0, 1, 1, 1, 1, 0, 1, 1, -1, 1, 0, -1, -1, -1, 1, 0, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, -1, 1, 1, 1
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OFFSET
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0,1
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COMMENTS
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The number of -1's among the four terms following the 0 at a(5*k), for k >= 0, is 1, 2, 3, 3, 1, 0, 3, 2, 2, 1, 4, 4, 0, 1, 3, 3, 1, 1, 3, 4, ...
See the Weisstein link, where it is stated that the period length is 0.
In general, the sequence {(k/n)} is not periodic if and only if k == 3 (mod 4). - Jianing Song, Dec 30 2018
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LINKS
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Eric Weisstein's World of Mathematics, Kronecker Symbol (contains this sequence).
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FORMULA
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Completely multiplicative with a(2) = -1, a(5) = 0, a(p) = 1 if p == 1, 3, 7, 9 (mod 20), a(p) = -1 if p == 11, 13, 17, 19 (mod 20). - Jianing Song, Dec 30 2018
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MAPLE
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0, seq(numtheory:-jacobi(-5, n), n=1..89); # Peter Luschny, Dec 30 2018
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MATHEMATICA
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Table[KroneckerSymbol[-5, n], {n, 0, 89}].
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PROG
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CROSSREFS
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Cf. A035183 (inverse Moebius transform).
Sequences related to Kronecker symbols that do not form a Dirichlet character: this sequence {(-5/n)}, A034947 {(-1/n)}, A091338 {(3/n)}, A089509 {(7/n)}.
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KEYWORD
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sign,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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