The series which forms the basis of all the other series is:- 1,2,4,8,16,18. Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by the following method:-
Step 1:- You definitely need "1". Step 2:- You need two and also 3. So, the next numbers is 2. Step 3:- Now you have 1,2. So, the next numbers is 4. Step 4:- Now you have 1,2,4. So, the next numbers is 8 Step 5:- Now you have 1,2,4,8. So, the next numbers is 16 Step 6:- Now you have 1,2,4,8,16. So, the next numbers is 18 So the series is 1,2,4,8,16,18.
My Question:- I don't know how to prove that there are more ( or exactly these many ) rigorously ( and why ). Any help would be appreciated.