Let the sequence be defined recursively in the following way for :

and for

Is ?

The conjecture is proven to be true.

See

http://arxiv.org/abs/1008.1409

and also the discussions:

Logarithm reciprocal

True or false logarithm

There is also a result-less (as of this writing) thread in sci.math.research and sci.math called "Logarithm reciprocal".

and for

Is ?

The conjecture is proven to be true.

See

http://arxiv.org/abs/1008.1409

and also the discussions:

Logarithm reciprocal

True or false logarithm

There is also a result-less (as of this writing) thread in sci.math.research and sci.math called "Logarithm reciprocal".