A362533 Decimal expansion of lim_{n->oo} ( Sum_{k=2..n} 1/(k * log(k) * log log(k)) - log log log(n) ).

2, 6, 9, 5, 7, 4

Offset

1,1

Comments

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.

Note that ( log log log(x) )' = 1 / ( x * log(x) * log log(x) ).

Links

Table of n, a(n) for n=1..6.

Patrice Lassère, Divergence douce de Sum_{k>1} 1/( k*log(k)*log log(k) ) par le TAF, Les-Mathematiques.net.

Formula

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).

Example

2.69574...

Crossrefs

Cf. A001620, A361972.

Sequence in context: A021375 A190407 A057052 * A346406 A078437 A372363

Adjacent sequences: A362530 A362531 A362532 * A362534 A362535 A362536

Keyword

nonn,cons,more

Author

Bernard Schott, Apr 24 2023

Status

approved