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A118582
Decimal expansion of Sum_{k>=3} 1/(k log k (log log k)^2).
2
3, 8, 4, 0, 6, 7, 6, 8, 0, 9, 2, 8, 2, 1, 7
OFFSET
2,1
COMMENTS
"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"
REFERENCES
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.
LINKS
R. J. Mathar, The series limit of sum_k 1/[k log k (log log k)^2], arXiv:0902.0789 [math.NA].
Eric Weisstein's World of Mathematics, Convergent Series
EXAMPLE
38.4067...
MATHEMATICA
(* 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 *)
CROSSREFS
Cf. A115563.
Sequence in context: A281516 A281630 A278957 * A356580 A086179 A185453
KEYWORD
cons,more,nonn
AUTHOR
Robert G. Wilson v, May 16 2006
EXTENSIONS
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
STATUS
approved