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A205325 Decimal expansion of the limit of [0;1,1,...] + [0;2,2,...] + ... + [0;n,n,...] - log(n) as n approaches infinity. 1
0, 4, 1, 6, 6, 6, 2, 6, 2, 7, 6, 3, 4, 8, 4, 8, 1, 0, 8, 7, 0, 1, 1, 6, 3, 5, 8, 5, 6, 9, 2, 3, 2, 0, 7, 4, 3, 1, 2, 5, 4, 5, 4, 6, 7, 5, 2, 8, 4, 1, 6, 3, 1, 8, 0, 9, 2, 0, 1, 3, 5, 9, 2, 3, 2, 9, 9, 1, 6, 4, 5, 7, 7, 5, 1, 2, 6, 2, 5, 5, 3, 7, 8, 3, 9, 5, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..87.

Martin Janecke, Edle Reihe

FORMULA

lim_{n->infinity} (1/[1;1,...] + 1/[2;2,...] + 1/[3;3,...] + ... + 1/[n;n,...] - log(n)).

lim_{n->infinity} (sum_{k=1...n} (2/(k + sqrt(k^2 + 4))) - log(n)).

EXAMPLE

0.0416662....

MATHEMATICA

digits = 10; dn = 1000000; Clear[f]; f[n_] := NSum[2/(k + Sqrt[k^2+4]) - 1/k, {k, 1, Infinity}, NSumTerms -> 200000, WorkingPrecision -> digits+10, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 20}}] + EulerGamma // RealDigits[#, 10, digits+2]& // First; f[dn]; f[n = 2*dn]; While[f[n] != f[n-dn], n = n+dn]; Prepend[ f[n][[1 ;; digits]], 0] (* Jean-François Alcover, Feb 25 2013 *)

CROSSREFS

Cf. A001620, A205326, continued fractions A001622, A014176, A098316, A098317, A098318.

Sequence in context: A110312 A011242 A008565 * A021100 A021028 A193529

Adjacent sequences:  A205322 A205323 A205324 * A205326 A205327 A205328

KEYWORD

cons,nonn

AUTHOR

Martin Janecke, Jan 26 2012

EXTENSIONS

More terms from Jean-François Alcover, Feb 25 2013

More terms from Jon E. Schoenfield, Jan 05 2014

STATUS

approved

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Last modified October 19 11:41 EDT 2018. Contains 316359 sequences. (Running on oeis4.)