teD,

I think we've almost got it...

repdigit - A number composed of a single digit is called a repdigit. If the digits are all 1s, the repdigit is called a repunit. The beast number 666 is a repdigit.

(technically then, 1,11,111... are repunits in decimal; 1,9,73... in octal (when converted to decimal); 1,3,7... in binary (again, converted); etc.)

this still doesn't quite cover the 9/9/99 form.