Yesterday, the best answer is: 2x-ceil(sqrt(-2x))+sqrt(-x).  (Contributed by fire. Good Job!)
fire solved the puzzle at 00:05:57.811; length: 32
turtle solved the puzzle at 15:14:57.022; length: 32
turtle solved the puzzle at 15:15:04.117; length: 31
turtle solved the puzzle at 15:15:05.503; length: 31
turtle solved the puzzle at 15:15:10.946; length: 30