Hello Math-fun, a little puzzle slightly adapted from here (in French), thanks to my friend Alexandre Wajnberg: http://dev.ulb.ac.be/urem/IMG/pdf/PRO12102010.pdf For any natural number "n" (base-10-written) we build "next-n" like this: - write the quantity of digits of "n" - concatenate the quantity of even digits in "n" - concatenate to the former concatenation the quantity of odd digits in "n" Example for "n" = 80322057626942 - there are 14 digits in "n": --> 14 - there are 10 even digits in "n": --> 1410 - there are 4 odd digits in "n": --> 14104 If we iterate the construction, we get the sequence: 80322057626942, 14104, 532, 312, 312, 312, ... Another example: 5771, 404, 330, 312, 312, 312, ... Is 312 the end of all such sequences? Best, É.