If we calculate the continued fraction of Champerowne's number $$0.1234567891011121314151617181920\cdots $$ it turns out that it contains very large entries
How can I understand this intuitively ?
The decimal representation of Champerowne's number must have parts which make the number look like a rational because of appearing periods, but it is not obvious where these (large) periods should be.
Many zeros (making the number look like to have a terminating decimal expansion) occur later, so they do not explain the large entries.
Any ideas ?