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A344716
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Decimal expansion of (gamma + log(4/Pi))/2, where gamma is Euler's constant.
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1
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4, 0, 9, 3, 9, 0, 0, 7, 0, 0, 8, 6, 0, 1, 1, 6, 5, 2, 6, 4, 8, 7, 7, 4, 4, 9, 0, 8, 2, 2, 8, 4, 8, 4, 2, 7, 7, 7, 2, 9, 3, 2, 3, 9, 5, 8, 7, 2, 5, 6, 1, 2, 6, 7, 7, 6, 6, 7, 5, 2, 0, 9, 1, 1, 9, 9, 7, 5, 8, 6, 0, 0, 4, 1, 6, 1, 1, 4, 0, 1, 1, 1, 8, 2, 5, 2, 5, 2, 2, 3, 5, 0, 4, 5, 4, 7, 2, 0, 8, 4, 4, 8, 3, 1, 2
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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 (A001620 + A094640)/2, the mean of Euler's constant and alternating Euler's constant.
Equals Sum_{n>=1} A000120(n) / (2*n*(2*n+1)), where A000120 is the number of 1-bits of n in binary. [Allouche, Shallit, Sondow]
Equals Sum_{k>=1} (1/(2*k-1) - log(1+1/(2*k-1))). - Amiram Eldar, Jun 19 2023
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EXAMPLE
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0.40939007008601165264877449082284842...
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MATHEMATICA
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RealDigits[(EulerGamma + Log[4/Pi])/2, 10, 100][[1]] (* Amiram Eldar, May 27 2021 *)
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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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