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A086311
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Decimal expansion of constant appearing in the variance for searching in a digital tree.
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3
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2, 8, 4, 4, 3, 8, 3, 1, 6, 8, 1, 1, 6, 7, 5, 6, 1, 6, 8, 2, 1, 6, 2, 2, 5, 7, 2, 3, 1, 4, 1, 0, 0, 8, 2, 6, 6, 4, 8, 9, 0, 3, 8, 5, 3, 0, 9, 0, 8, 7, 1, 0, 7, 7, 4, 3, 9, 5, 5, 3, 7, 5, 4, 6, 6, 6, 3, 6, 8, 1, 9, 0, 2, 3, 9, 4, 2, 4, 1, 2, 7, 7, 7, 4, 8, 8, 2, 1, 9, 5, 7, 9, 1, 7, 1, 8, 4, 8, 8, 0, 2, 5
(list;
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refs;
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text;
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 356.
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LINKS
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FORMULA
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1/12 + (Pi^2+6)/(6*log(2)^2) - alpha - beta, where gamma is Euler's constant, alpha is the Erdős-Borwein constant (A065442) and beta is A065443. - Jean-François Alcover, Jul 29 2014, after Steven Finch
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EXAMPLE
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2.84438316811675616821622572314100826648903853090871...
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MATHEMATICA
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digits = 102; alpha = NSum[1/(2^k-1), {k, 1, 500}, NSumTerms -> 100, WorkingPrecision -> digits+10]; beta = NSum[1/(2^k-1)^2, {k, 1, 500}, NSumTerms -> 100, WorkingPrecision -> digits+10]; RealDigits[1/12 + (Pi^2+6)/(6*Log[2]^2) - alpha - beta, 10, digits] // First
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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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