A099870 Decimal expansion of Sum_{n>0} 1/(n^log(n)).

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

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 29 2004

Keywords

• nonn
• cons

Comments

This series converges slowly. - Bernard Schott, May 23 2019

This series converges more slowly than Sum_{n>=0} 1/a^n for every a > 1 but faster than Sum_{n>=1} 1/n^p for every p > 1. - Jianing Song, Jul 25 2021

Examples

			2.23818130679669304318313699419971800961618108176500542239159050811...
		

References

• J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, Exercice 9c, page 293.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073009, A099871.

Programs

Magma

SetDefaultRealField(RealField(100)); [(&+[1/k^Log(k): k in [1..1000]])]; // G. C. Greubel, Nov 20 2018

Maple

evalf(sum(1/(n^log(n)), n=1..infinity), 110); \\ Bernard Schott, May 23 2019

Mathematica

s = 0; Do[s = N[s + 1/n^Log[n], 256], {n, 10^7}]; RealDigits[s, 10, 111][[1]] (* Robert G. Wilson v, Nov 02 2004 *)

PARI

default(realprecision,35);sum(n=1,50000,1./(n^log(n)))

PARI

sumpos(n=1, 1/(n^log(n))) \\ Michel Marcus, May 24 2019

Sage

numerical_approx(sum(1/k^log(k) for k in [1..1000]), digits=100) # G. C. Greubel, Nov 20 2018

Formula

Equals Sum_{n>=1} 1/(n^log(n)).

Extensions

More terms from Robert G. Wilson v, Nov 02 2004