The number one million can be presented by 2 digits : 1000000, i.e. a chain of 7 digits.
Another possibility is 1000². 3 distinct digits, 5 characters. I

You are requested to express one million, using a single digit d plus some operators creating a chain of n characters ( digits and operators).
What digit is your choice and how low is the minimal n?

a). The permissible operators are : + - * / and ^.

b). Sqrt and ! are allowed as well.”

. REM: count digits and operators only, ignore ^, concatenation and brackets; e.g. (77-7)/7 is counted as 6.