Let S be the set of positive integers that can be written as a sum of one or more 4's and/or 7's. For case, 7 e S (in set) and 18 e S (because 18 = 4+7+7).

It turns out that S contains all positive integers except for some relatively small missing values.

Question 1- What is the greatest integer g that is not in S? Just write down the answer, you don't have to show your work here or prove that g is not in S.

Question 2- Prove using mathematical induction that all integers greater than g are elements of S.

I was eager someone can describe on a high level as to how this happens.