Hello Math-fun, Let's say a(n) = 329441. How do we build a(n+1)? First, sum, from left to right, the absolute differences of a(n)'s digits: a(n) = 3 2 9 4 4 1 abs. diff = 1+7+5+0+3 = 16 Now add this sum to a(n) so to produce a(n+1): 329441 + 16 = 329457 = a(n+1) And repeat: 329457 + 16 = 329473 329473 + 20 = 329493 329493 + 24 = 329517 329517 + 22 = 329539 etc. The sequence stops when all digits off a(n) are the same, of course: If we start with 18, for instance, we have: S = 18, 25, 28, 34, 35, 37, 41, 44, 44, 44, ... Are there integers leading to infinite sequences? If yes, what would be the smallest one? Best, É. (hoping, as usual, that this is not old hat)