Hello Seqfan and math-fun, Take an integer like 36, for example. Concatenate an infinite amount of copies. You get: 363636363636363636363636363636... - read the leftmost digit -"3"-, - jump *over* 3 digits (to the right), land on (3) and erase it: 3636(3)6363636363636363636363636... ^ - read the leftmost unread digit, jump only visible digits, erase: 3636(3)6363(6)36363636363636363636... ^^ - repeat until you see a substring like this [...(a)36(b)...] [(a) and (b) are erased digits - "36" is the integer you are, testing]: bingo, you have found a "Self-erasure survi- ving number" (SESN): "36" is such a number: 3636(3)63(6)3(6)36(3)(6)3(6)36363636363636... ^^^^ ^^ .. <-- hit This erasing technique gives sometimes quite complicated pat- terns. "16", for instance, is not a SESN -- but it takes a while to see: 16(1)616(1)61(6)1(6)(1)6(1)(6)1(6)1(6)1(6)1(6)(1)6(1)616(1)61(6)1(6) ^^ ^^^ ^^ ^ ^ ^ ^ ^ ^ ^ ^^^ ^^ ^ |_______________________________________________| recurrent pattern The first SESN I have found by hand are: 0 1 2 3 4 5 6 7 8 9 10 20 23 24 25 26 27 28 29 30 32 36 37 38 39 40 42 ... [BTW, reading "0" means erasing the closest visible digit immediately to the right] No SESN > 10 begins with "1" -- see why? No SESN > 29 begins with "2", etc. The sequence is finite, thus. Last term? And what about recurrent patterns: do all integers behave like that? Could some strings be definitely "chaotic"? I guess no... Best, É.