Gottfried Wrote:On the other hand, it should arrive at 3^(1/3)...

Do I actually overlook something and the sequence can indeed cross e^(1/e)?

Indeed a very interesting observation, Gottfried.

You only arrive at the expected value if it is , i.e.

only if .

This is because for , where and .

For , for example , is always for each . Suppose otherwise then would , for while .