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

Author

Bernard Schott, Apr 24 2023

Keywords

• nonn
• cons
• more

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) ).

Examples

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Links

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

Crossrefs

Cf. A001620, A361972.

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).