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

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

Author

Jianing Song, Jul 28 2021

Keywords

• nonn
• cons

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.

Examples

			2.07138435359817861835919830739134720946...
		

Links

• Jianing Song, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A099870, A099871, A073009.

Programs

PARI

sumpos(n=1, 1/(n^(log(n)^2)))