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A222183
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Decimal expansion of Sum_{k >= 0} 1/(4*k+1)^2.
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6
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1, 0, 7, 4, 8, 3, 3, 0, 7, 2, 1, 5, 6, 6, 9, 4, 4, 2, 1, 2, 0, 4, 4, 5, 7, 4, 4, 4, 9, 5, 8, 4, 5, 1, 5, 0, 1, 3, 4, 4, 1, 8, 0, 9, 0, 0, 0, 9, 3, 3, 8, 5, 4, 8, 1, 2, 8, 4, 0, 8, 3, 3, 9, 5, 8, 2, 4, 6, 3, 4, 3, 1, 1, 2, 8, 9, 3, 2, 7, 7, 1, 2, 4, 2, 7, 2, 8
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OFFSET
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1,3
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LINKS
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FORMULA
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Equals -Integral_{x=0..1} log(x)/(1 - x^4) dx. - Amiram Eldar, Jul 17 2020
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EXAMPLE
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1.074833072156694421204457444958451501344... = 1 + 1/25 + 1/81 + 1/169 + 1/289 + ...
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MATHEMATICA
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RealDigits[Catalan/2 + Pi^2/16, 10, 90][[1]] (* or *) RealDigits[PolyGamma[1, 1/4]/16, 10, 90]
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PROG
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(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (8*Catalan(R) + Pi(R)^2)/16; // G. C. Greubel, Aug 23 2018
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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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