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A372386
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Decimal expansion of Sum_{k>=0} (k^2+1) / (k^4+1).
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1
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2, 7, 0, 7, 0, 0, 5, 5, 0, 4, 3, 9, 1, 4, 4, 6, 9, 2, 3, 7, 3, 0, 0, 8, 0, 8, 2, 6, 9, 9, 5, 4, 4, 7, 6, 6, 8, 7, 3, 3, 0, 9, 9, 0, 1, 5, 7, 1, 9, 9, 7, 3, 1, 6, 2, 5, 4, 4, 1, 2, 0, 5, 8, 8, 0, 4, 9, 9, 3, 4, 0, 3, 6, 6, 5, 2, 2, 2, 2, 4, 6, 0, 0, 4, 2, 3
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals 1/2 - Pi*sinh(sqrt(2)*Pi)/(sqrt(2)*(cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))). - Vaclav Kotesovec, May 14 2024
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EXAMPLE
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2.70700550439144692373008082699544766873309901571997...
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MATHEMATICA
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s = Sum[ (k^2 + 1)/(k^4 + 1), {k, 0, Infinity}]
d = Chop[N[s, 100]]
First[RealDigits[d]]
RealDigits[1/2 - Pi*Sinh[Sqrt[2]*Pi]/(Sqrt[2]*(Cos[Sqrt[2]*Pi] - Cosh[Sqrt[2]*Pi])), 10, 120][[1]] (* Vaclav Kotesovec, May 14 2024 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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