OFFSET
1,1
COMMENTS
An infinite sum that converges faster than A099870.
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.
LINKS
Jianing Song, Table of n, a(n) for n = 1..1000
EXAMPLE
2.07138435359817861835919830739134720946...
PROG
(PARI) sumpos(n=1, 1/(n^(log(n)^2)))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Jul 28 2021
STATUS
approved