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A145420 Decimal expansion of sum_{n=2...infinity} 1/(n* (log n)^4). 0
2, 5, 5, 9, 1, 1, 9, 7, 4, 2, 9, 8, 6, 7, 3, 1, 4, 1, 8, 5, 7, 2, 0, 2, 0, 9, 7, 0, 3, 1, 0, 7, 6, 2, 9, 3, 3, 6, 1, 9, 1, 7, 8, 1, 5, 6, 3, 6, 6, 8, 7, 9, 4, 8, 7, 1, 7, 0, 6, 7, 9, 7, 0, 7, 9, 1, 4, 6, 5, 9, 0, 9, 8, 1, 6, 6, 1, 7, 1, 7, 6, 6, 5, 9, 3, 7, 9, 5, 9, 9, 2, 4, 9, 0, 3, 2, 1, 3, 8, 3, 5, 5, 4, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Quartic analog of A115563. Evaluated by direct summation of the first 160 terms and accumulating the remainder with the 5 nontrivial terms in the Euler-Maclaurin expansion.

LINKS

Table of n, a(n) for n=1..105.

R. J. Mathar, The series limit of sum_k 1/[k log k (log log k)^2], arXiv:0902.0789 (2009), last sentence.

EXAMPLE

2.5591197429867314185720209

MATHEMATICA

(* Computation needs a few minutes *) digits = 105; NSum[ 1/(n*Log[n]^4), {n, 2, Infinity}, NSumTerms -> 800000, WorkingPrecision -> digits + 5, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 10}}] // RealDigits[#, 10, digits] & // First (* Jean-François Alcover, Feb 12 2013 *)

CROSSREFS

Cf. A115563.

Sequence in context: A076520 A014249 A168071 * A284169 A152781 A200242

Adjacent sequences:  A145417 A145418 A145419 * A145421 A145422 A145423

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Feb 08 2009

EXTENSIONS

More terms from Jean-François Alcover, Feb 12 2013

STATUS

approved

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Last modified November 14 20:15 EST 2019. Contains 329130 sequences. (Running on oeis4.)