Shouldn't sequence A036788 be keyworded "fini"?

[Andrew Weimholt]

On 7/2/08, Jonathan Post <jvospost3 at gmail.com> wrote:
> Shouldn't sequence A036788 be keyworded "fini" for "finite"?
>
>  A036788  Length of Roman notation for n <= length of decimal representation.
[...]
>  Alternatively, the parentheses can be nested so ( I )  is
>  1,000 and  ( ( I ) ) is 1,000,000. The numbers can get a bit unwieldy
>  as they get bigger.

Adding two characters,  "(" and ")", for each 1000, is still shorter
than writing
three characters, "000", so the sequence would be infinite if you allow for
arbitrarily deep nesting of parenthesis.

for example...
   ( I ) is shorter than 1000 by 1 character
   (( I )) is shorter than 1000000 by 2 characters
   ((( I ))) is shorter than 1000000000 by 3 characters
  ...
  The similar expansion for 10^(3n) is shorter than the decimal
representation by n charcters.

Andrew