Our task will be to represent all (or *almost all* - as explained below) integers from 1 to n using some or all of the initial triplet and any quantity of operations defined above.

So:

1=1

6=1+5

9=5*2-1

13=15-2

27=51-4!

60=12*5 etc

Let's define n as the first occurrence of not being able to find a valid representation for n+1 and for n+2. I believe that in our case n=17 (15+2), since neither 18 nor 19 get valid solutions.

**
You are requested to find a triplet of integers (a,b,c) enabling a maximal n.**