There are additional numbers fitting the definition below:
a. The number is a positive integer of more than 1 digit.
b. Its value remains unchanged if some of the operations ^,* are introduced between its digits.
c. Absence of any of the above signs between 2 adjacent digits signifies their concatenation.
d. Leading zeroes within an exponent are allowed.
e. Brackets may be added to define the order of operations.
9509900499 = 95^0*99^004*99.
(i)Prove that there is infinite number of "printer's glitch" numbers.
(ii) List all such numbers below 400,000.