login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115563 Decimal expansion of Sum_{n>=2} 1/(n*log(n)^2). 6
2, 1, 0, 9, 7, 4, 2, 8, 0, 1, 2, 3, 6, 8, 9, 1, 9, 7, 4, 4, 7, 9, 2, 5, 7, 1, 9, 7, 6, 1, 6, 5, 5, 1, 3, 2, 6, 3, 8, 5, 5, 3, 1, 9, 8, 4, 3, 9, 4, 7, 4, 2, 0, 2, 2, 6, 4, 9, 9, 1, 5, 6, 0, 3, 1, 9, 2, 8, 1, 4, 6, 9, 4, 9, 3, 9, 1, 3, 6, 8, 7, 4, 1, 7, 7, 1, 6, 9, 2, 9, 1, 3, 7, 7, 1, 8, 6, 2, 3, 2, 1, 3, 5, 8, 3, 8, 7, 6, 6, 5, 3, 4, 7, 2, 6, 0, 9, 7, 3, 8, 9, 0, 3, 5, 7, 7, 9, 5, 0, 8, 6, 5, 9, 4, 8, 9, 4, 2, 4, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum_{n>1} 1/(n*log(n)^2) is a tiny bit more than (zeta(2))^(3/2) =

  (Pi^2 / 6)^(3/2) = 2.109709908063657.... - Daniel Forgues, Mar 30 2012

LINKS

Table of n, a(n) for n=1..141.

John V. Baxley, Euler's constant, Taylor's formula, and slowly converging series, Math. Mag. 65 (1992), 302-313.

Bart Braden, Calculating sums of infinite series, Am. Math. Monthly 99 (1992) 649-655.

David Broadhurst, Re: need help about 2 constants, primeforum, Mar 20 2006

Rick Kreminski, Using Simpson's rule to approximate sums of infinite series, College Math. J. 28 (1997), 368-376.

R. J. Mathar, The series limit of sum_k 1/[k*log k *(log log k)^2], arXiv:0902.0789, App. A.

Eric Weisstein's World of Mathematics, Convergent Series

EXAMPLE

2.10974280123689197447925719761655132638553198439474202264991560319281...

MATHEMATICA

digits = 150; NSum[1/(n*Log[n]^2), {n, 2, Infinity}, NSumTerms -> 200000, WorkingPrecision -> digits + 5, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 20}}] (* Vaclav Kotesovec, Mar 01 2016, after Jean-Fran├žois Alcover *)

CROSSREFS

Cf. A145419, A137245, A257812. A097906 is a similar sum.

Sequence in context: A158335 A111595 A021478 * A293881 A185285 A268434

Adjacent sequences:  A115560 A115561 A115562 * A115564 A115565 A115566

KEYWORD

cons,nonn

AUTHOR

Pierre CAMI, Mar 11 2006

EXTENSIONS

Removed incorrect speculations about relations to A097906 - R. J. Mathar, Oct 14 2010

More terms from Robert G. Wilson v, Dec 12 2012

Corrected a(55) an beyond, Vaclav Kotesovec, Mar 01 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 14:33 EST 2017. Contains 294894 sequences.