Let's start with a triplet of integers, say (1, 2, 5) and a set of mathematical operations (+, , *, /, ^, sqrt, fact!, concatenation, brackets).
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*21
13=152
27=514!
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.
(In reply to
re(2): some hints & remarks @ Ch by Ady TZIDON)
I agree with Dej Mar, there were only 9 mathematical operations. If factorials are a family, why not roots as well? And square brackets could be a family that includes floor or ceiling (especially floor, as in many instances it's understood that the square brackets signify floor without even leaving out the top horizontal bar).
BTW, my first post's result was based on 4, 7 and 9 because the bug caused stopping at the first total number of failures exceeding 2. I first fixed that bug and redid 4, 7, 9. Later I ran the full set of combinations to come out with 4, 9 and 9. This latter has a lot of holes but the first two in a row come later.

Posted by Charlie
on 20200911 07:38:31 