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