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A196554
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Decimal expansion of Sum_{i>=0} 1/((8*i+1)*(8*i+5)).
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1
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2, 1, 6, 7, 4, 3, 2, 4, 6, 8, 3, 4, 9, 7, 7, 7, 5, 9, 3, 9, 3, 4, 9, 8, 7, 9, 0, 9, 7, 0, 7, 1, 7, 6, 7, 8, 4, 1, 3, 0, 4, 3, 8, 4, 1, 8, 3, 6, 3, 1, 1, 2, 2, 6, 0, 8, 3, 7, 5, 7, 9, 5, 9, 7, 2, 9, 4, 0, 9, 8, 3, 7, 8, 5, 2, 7, 3, 5, 3, 3, 2, 2, 6, 3, 9, 3, 7
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals sqrt(2)*(Pi + log(3 + 2^(3/2)))/32.
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EXAMPLE
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0.21674324683497 = 1/5 + 1/117 + 1/357 + 1/725 + 1/1221 + 1/1845 + ...
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MAPLE
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sqrt(2)/32*(Pi+log(3+2*sqrt(2))) ; evalf(%) ;
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MATHEMATICA
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RealDigits[(Sqrt[2]/32)(Pi + Log[3 + 2 Sqrt[2]]), 10, 74][[1]] (* Bruno Berselli, Dec 20 2011 *)
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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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