I have a problem with SIFT that I do not understand. Lowe  proposed in his work the
s=3 levels of scale are enough for one octave. Afterwards, he mentioned that you need to compute
Why there are 3 and not 2 additional levels required. I understand that you require one additional level above and one additional level below the scales since you search for extrema in neighbored scales.
For what is the third additional level of scale?
Thank you very much in advance!
 Distinctive Image Features from Scale-Invariant Keypoints D. G. Lowe Int. Journal of Computer Vision 60(2) (2004), pp. 91--110