Hello Math-Fun, Infinite loop: a) 12 - 12 - 12 - 12 - 12 ... Shortest loops so far: b) 6 - 10 - 15 - 14 - 11 - 8 - (6) c) 6 - 10 - 16 - 17 - 13 - 8 - (6) A longer loop: d) 6 - 10 - 15 - 14 - 12 - 11 - 8 - (6) A combination of (c) and (d): e) 6 - 10 - 16 - 17 - 13 - 8 - 6 - 10 - 15 - 14 - 12 - 11 - 8 - (6) This loop (e) shows ten different "words". The rule is: i) Replace all integers by their English spelling ii) a(n) is the count of the letters used by a(n)+a(n+1) Example for (d): d) 6 - 10 - 15 - 14 - 12 - 11 - 8 - (6) d) six-ten-fifteen-fourteen-twelve-eleven-eight-(six) Letters: 3 3 7 8 6 6 5 3 Letter-sum: 6 10 15 14 12 11 8 ... this being the sequence itself. Is it possible to find more loops? To insert more words not already used above? Best, É.