cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A099870 #30 Sep 08 2022 08:45:15
%S A099870 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,
%T A099870 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,
%U A099870 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
%N A099870 Decimal expansion of Sum_{n>0} 1/(n^log(n)).
%C A099870 This series converges slowly. - _Bernard Schott_, May 23 2019
%C A099870 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
%D A099870 J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, Exercice 9c, page 293.
%H A099870 G. C. Greubel, <a href="/A099870/b099870.txt">Table of n, a(n) for n = 1..1000</a>
%F A099870 Equals Sum_{n>=1} 1/(n^log(n)).
%e A099870 2.23818130679669304318313699419971800961618108176500542239159050811...
%p A099870 evalf(sum(1/(n^log(n)), n=1..infinity), 110); \\ _Bernard Schott_, May 23 2019
%t A099870 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 *)
%o A099870 (PARI) default(realprecision,35);sum(n=1,50000,1./(n^log(n)))
%o A099870 (PARI) sumpos(n=1, 1/(n^log(n))) \\ _Michel Marcus_, May 24 2019
%o A099870 (Magma) SetDefaultRealField(RealField(100)); [(&+[1/k^Log(k): k in [1..1000]])]; // _G. C. Greubel_, Nov 20 2018
%o A099870 (Sage) numerical_approx(sum(1/k^log(k) for k in [1..1000]), digits=100) # _G. C. Greubel_, Nov 20 2018
%Y A099870 Cf. A073009, A099871.
%K A099870 nonn,cons
%O A099870 1,1
%A A099870 Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 29 2004
%E A099870 More terms from _Robert G. Wilson v_, Nov 02 2004