A103430 Decimal expansion of integral(1/(n*log(n))^(3/2),n=2..Inf).

6, 8, 3, 2, 1, 8, 5, 9, 7, 1, 7, 6, 0, 4, 7, 3, 8, 2, 1, 7, 9, 3, 2, 0, 3, 9, 0, 3, 0, 1, 9, 5, 2, 6, 6, 2, 8, 9, 4, 0, 0, 7, 6, 5, 2, 1, 8, 6, 9, 7, 7, 4, 4, 9, 9, 5, 1, 1, 5, 4, 0, 4, 7, 6, 9, 1, 8, 3, 5, 1, 5, 6, 8, 4, 1, 8, 5, 2, 8, 0, 0, 0, 5, 9, 6, 2, 8, 4, 9, 6, 7, 9, 0, 7, 3, 3, 8, 3, 1, 8, 1, 1, 0, 7, 5

Offset

0,1

Comments

"...the probability of m belonging A103359 is roughly 1/(n*ln(n)^(3/2)) and integral(1/(n*ln(n)^(3/2)),n=2..oo) is finite" - Max [rel(AT)funn.ac.ru] in seqfan [seqfan(AT)ext.jussieu.fr] posting Feb 03 2005

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

Integral(1/(n*log(n))^(3/2), n=2..inf) = sqrt(2)(1/sqrt(log 2) - sqrt(Pi)*erfc(sqrt(log(2)/2))).

Example

0.6832185971760473821793203903019526628940076521...

Mathematica

(2 - Erfc[Sqrt[Log[2]/2]]*Sqrt[Pi*Log[16]])/Sqrt[Log[4]] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 19 2013 *)

Crossrefs

Cf. A103359.

Sequence in context: A197267 A019255 A153895 * A097880 A196768 A355976

Adjacent sequences: A103427 A103428 A103429 * A103431 A103432 A103433

Keyword

easy,nonn,cons

Author

Zak Seidov, Feb 05 2005

Extensions

Typo in formula fixed by Jean-François Alcover, Feb 19 2013

Status

approved