[cgratocc] product of shifted iterated logarithms

each term has value 1 at n = 0:

f1(n) = (n+1) * log(n + e) * log log(n + e^e) * log log log(n + e^e^e) * ...

or, each term has value 1 at n = 1:

f2(n) = n * log(n * e) * log log(n * e^e) * log log log(n * e^e^e) * ...

does the product converge for n>0 or n>1 respectively?  integrate 1/f from n=0 or n=1 respectively to infinity.  does it diverge?

previously on iterated log.