Hello Math-Fun and SeqFan, Start with 1, then a(n) is the smallest integer not used so far whose leftmost digits show the sum of a(n-1)'s digits: 1,10,11,2,20,21,3,30,31,4,40,41,5,50,51,6,60,61,7,70,71,8,80,81, 9,90,91,100,12,32,52,72,92,110,22,42,62,82,101,23,53,83,111,33, 63,93,120... This infinite seq. is certainly a rearrangement of the natural integers. Starting with my birthday year produces: 1951,16,7,70,71,8,80,81,9,90,91,10,1,11,2,20,21,... The present year gives: 2007,9,90,91,10,1,11,2,20,21,3,30,31,... Will the 1951-sequence and the 2007-sequence merge with the first one, sooner or later? This is the 11-sequence: 11,2,20,21,3,30,31,4,40,41,5,50,51,6,60,61,7,70,71,8,80,81,9,90, 91,10,1,12... 12 is there because 11 is forbidden; we could thus assign to 11 a "pseudo-loop" length -- the number of integers which separate the starting "11" from his expected second appearance. Here, this pseudo-loop has length 27. Could someone compute a few pseudo-loop lenghtes (say for n=1 to n=200)? This seq. obviously begins like this (n=1 to n=11): 1,1,1,1,1,1,1,1,1,2,27... Best, É.