
Question Definitions: For
: Let
be the last
such that the i'th iteration of log composition on
is still above 1.




Remark: K(n) is the "towerian log" where and
.
Let where the last log is iterated
times.
PROBLEM : Is . convergent or divergent.
REMARKS: The log could be in base 2 this clearly does not affect the result.
The log could be replaced by ceil(log) or floor(log) , this may affect the result.
MOTIVATION: the sum of ( harmonic serie is divergent) , the same is true with
and
etc (called bertrand series I think) .
HISTORY: I made it up, it should have been thought of somewhere else (my culture in analysis is small).