I was informed the correct formula to solve the puzzle is as follows.
11a = (11 x a) + 2 = n, such that...
111 = (11 x 1) + 2 = 13
112 = (11 x 2) + 2 = 24
and so on until
118 = (11 x 8) + 2 = 90
119 = (11 x 9) + 2 = 101
And as I said I got it wrong. I used Carl's second algorithm, where 11 is multiplied by the given variable and then you add the sum of the digits.
"Carl's Second Algorithm" does sound like something from a dusty old physics book, doesn't it? Right up there with Newton's Second law of Thermodynamics.