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A210245
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Signs of the polylogarithm li(-n,-1/2).
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3
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1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1
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OFFSET
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0
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COMMENTS
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Given an integer n, consider the infinite series s(n) = li(-n,-1/2)) = Sum((-1)^k)(k^n)/2^k) for k=0,1,2,... Then the value of a(n) is the sign of s(n).
Should s(n) be 0, the sign would be set to 0 as well. However, it is not known whether this ever happens.
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LINKS
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FORMULA
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a(n) is the same as the sign of cos((n+1)*arctan(Pi/log(2))). - Mikhail Kurkov, Apr 13 2021 [verification needed]
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EXAMPLE
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a(5) = sign(A212846(5)) = sign(-7) = -1.
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MATHEMATICA
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Join[{1}, Sign[PolyLog[-Range[80], -1/2]]] (* Harvey P. Dale, Jul 21 2024 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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