>
>
> I am pretty sure that such an implicit expression exists: it is << the
>> number of etc etc....
>>
>
> We do not speak of just the definition of what kind of number to find, but
> of the construction of finding the number (or already of a compression of
> its explicit digits).


It's hard to come up with a formal definition of "implicit expression"
which excludes the definition itself :-)  maybe something like a fast
algorithm for computing a given digit (this exists for pi
https://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml ).

(Well, it's fun, but I would not spend days on this :-) )
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