Hello Math-fun,, a light (iterating) idea (too light, I'm afraid)... Take an integer N (N = 1750 here) Make the sum of N's digits and call it D (D = 13 here) Now build the integers B (big) and S (small) like this: - B is the biggest integer you can write using one digit of N and all the digits of D (here 7 and 1,3 --> B = 731) - S is the smallest integer you can write using one digit of N and all the digits of D (here 0 and 1,3 --> S = 103) Now iterate, computing B, then S, then B, then S, etc. Let's see what happens, starting with 1 (the line under the sequence shows D (digit sum) then B (big), then D, then S (small), then D, then B, then D, then S, ... 1---11---12---32---25---75---125---85---135---95---145 1 B 2 S 3 B 5 S 7 B 12 S 8 B 13 S 9 B 14 S 145---510---16---76---136---610---17---87 ... S 10 B 6 S 7 B 13 S 10 B 7 S 8 B ... Where do we get? (loops, fixed points, flights, etc.) Best, É. (and what about iterating only B's? Or S's?)