A recent discussion on "Sequence Fanatics" has me thinking about a general process. Let An be any non-negative integer sequence. Derive Bn with the rule: B0 = A0 and for n > 0 Bn = B(n-1) - An if this is non-negative Bn = B(n-1) + An otherwise. If An is the non-negative integers (A001477), then Bn is A008344. If An is the perfect squares (A000290), then Bn is A076042. Question: Does A076042 ever revisit 0? If you play with it, you will see that the sequence is divided into eras where adding and subtracting strictly alternate. These eras are punctuated by an extra add when subtracting would go negative. The sequence reaches a local minimum just at the end of each era. If we define these minima as the last value in the sequence before a double add, they are: 1, 5, 5, 7, 4, 19, 104, 74, 193, 515, 725, 241 ... This sequence is not in OEIS, nor are any of its first few truncations. The indices of the minima are not present either. Intuitively, this sequence is aiming at 0 from greater and greater distances, and is unlikely to ever hit the bullseye. But I think the problem is amenable to more rigorous analysis. Can any funsters contribute additional insight?