I'm not a big fan of results peculiar to the decimal radix, but this reminds me of a Fortran compiler that Peter Samson wrote in PDP-6 machine language the late 60s, based on an absolutely inscrutable paper on generative grammars by Edgar T. Irons. Since the task of commenting the code would have been much larger than the coding itself, there was only one comment in the entire listing, where Peter needed the constant 1000. The line was ...: 1750 ;RIP JSB (The assembler default radix was octal. You had to add a decimal point if you wanted decimal. And Peter was a huge Bach fan.) --rwg ---------------------------- Original Message ---------------------------- From: "Eric Angelini" <Eric.Angelini@kntv.be> Date: Mon, September 19, 2011 2:20 pm -------------------------------------------------------------------------- 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, �. (and what about iterating only B's? Or S's?)