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*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.

(In reply to Record by Ady TZIDON)

As mentioned in my previous post, I had re-used a program used before, and I explicitly avoided using subfactorial and double factorial, as only factorial is mentioned in your list of valid functions. The code is there in the program but not called.

Posted by Charlie on 2020-09-10 20:58:48