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A346670 Decimal expansion of Sum_{n>=1} 1/(n^(log(n)^2)) = Sum_{n>=1} exp(-log(n)^3).

%I A346670 #14 Jul 31 2021 00:50:10
%S A346670 2,0,7,1,3,8,4,3,5,3,5,9,8,1,7,8,6,1,8,3,5,9,1,9,8,3,0,7,3,9,1,3,4,7,
%T A346670 2,0,9,4,6,0,9,8,2,4,7,8,2,3,7,4,9,9,6,0,2,9,6,9,1,9,0,5,6,1,9,3,3,4,
%U A346670 1,8,3,5,9,2,7,7,0,1,4,2,8,1,0,8,4,7,6,5,8,0,8,5,8,9,5,4,9,9,9,7,0,9,2,6
%N A346670 Decimal expansion of Sum_{n>=1} 1/(n^(log(n)^2)) = Sum_{n>=1} exp(-log(n)^3).
%C A346670 An infinite sum that converges faster than A099870.
%C A346670 Note that as p > 0 gets larger and larger, the series Sum_{n>=1} 1/(n^(log(n)^p)) converges faster and faster, but will always converge more slowly than Sum_{n>=0} 1/a^n for every a > 1.
%H A346670 Jianing Song, <a href="/A346670/b346670.txt">Table of n, a(n) for n = 1..1000</a>
%e A346670 2.07138435359817861835919830739134720946...
%o A346670 (PARI) sumpos(n=1, 1/(n^(log(n)^2)))
%Y A346670 Cf. A099870, A099871, A073009.
%K A346670 nonn,cons
%O A346670 1,1
%A A346670 _Jianing Song_, Jul 28 2021