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A118582
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Decimal expansion of Sum_{k>=3} 1/(k log k (log log k)^2).
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2
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3, 8, 4, 0, 6, 7, 6, 8, 0, 9, 2, 8, 2, 1, 7
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OFFSET
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2,1
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COMMENTS
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"The series [see title] converges to 38.43... so slowly that it requires 10^(3.14*10^86) terms to give two-decimal accuracy"
example 16 - "The series Sum_{k=3..inf} 1/(k log k (log log k) diverges, but the partial sums exceed 10 only after a googolplex of terms have appeared"
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REFERENCES
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Daniel Zwillinger, Editor, CRC Standard Mathematical Tables and Formulae, 31st Edition, Chapman & Hall/CRC, Boca Raton, 1.3.9 Miscellaneous Sums and Series, example 15, page 42, 2003.
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LINKS
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EXAMPLE
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38.4067...
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MATHEMATICA
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(* Computation needs a few minutes *) digits = 15; m0 = 10^6; dm = 10^5; Clear[f]; f[m_] := f[m] = Sum[ 1/(k*Log[k]*Log[Log[k]]^2) // N[#, digits+2]&, {k, 3, m}] + 1/Log[Log[m + 1/2]] // RealDigits[#, 10, digits+2]& // First; f[m0]; f[m = m0 + dm]; While[f[m] != f[m - dm], m = m + dm]; f[m][[1 ;; digits]] (* Jean-François Alcover, Mar 07 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Corrected the least significant digit and added 11 more digits. R. J. Mathar, Feb 03 2009
Name spelling and 3 least significant digits corrected by R. J. Mathar, Jul 07 2009
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STATUS
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approved
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