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.
%I A362533 #9 Apr 28 2023 22:38:12
%S A362533 2,6,9,5,7,4
%N A362533 Decimal expansion of lim_{n->oo} ( Sum_{k=2..n} 1/(k * log(k) * log log(k)) - log log log(n) ).
%C A362533 If u(n) = Sum_{k=2..n} ( 1/(k*log(k)*log log(k)) - log log log(n) ), then (u(n)) is convergent, while the series v(n) = Sum_{k=2..n} 1/(k*log(k)*log log log(k)) diverges (see link). This is an extension of A001620 and A361972.
%C A362533 Note that ( log log log(x) )' = 1 / ( x * log(x) * log log(x) ).
%H A362533 Patrice Lassère, <a href="https://les-mathematiques.net/serveur_exos/exercices/156/2885/">Divergence douce de Sum_{k>1} 1/( k*log(k)*log log(k) ) par le TAF</a>, Les-Mathematiques.net.
%F A362533 Limit_{n->oo} 1/( 2*log(2)*log log(2) ) + 1/( 3*log(3)*log log(3) ) + ... + 1/( n*log(n)*log log(n) ) - log log log(n).
%e A362533 2.69574...
%Y A362533 Cf. A001620, A361972.
%K A362533 nonn,cons,more
%O A362533 1,1
%A A362533 _Bernard Schott_, Apr 24 2023