Statement

Valerio was recently introduced to the concept of excellent numbers: a positive integer is considered excellent if its decimal representation only contains the digits 1 and 5, and it is divisible by 3. For example, 15 and 111 are excellent numbers (15 = 5* 3 + 0 and 111=37* 3 + 0), while 151 is not (151 = 50* 3 + 1). \footnotetextAn Angel Number, in Numerology, is a number with a predictable pattern that is believed to be a sign from the universe. Valerio is wondering if there exists at least one excellent number with exactly N digits. Help him by finding one, or by determining that there are no excellent numbers with that number of digits!