(05/01/2010, 03:21 PM)tommy1729 Wrote: dear mike
the regular interval that you seek has been computed by andy.
its somewhere here on this forum.
Lazy boy!
Andrew gave a rough overview of the behavior of the higher operations here.
Due to the fact that \( \operatorname{sexp}_b(x)\to -\infty \) (below identity) for \( x\to -2 \) and \( \operatorname{sexp}_b(0)=1 \) (above identity), tetration always (for every base) has a lower fixed point (I guess this is true for every even rank), which can be used for regular iteration giving a pentation (or the odd rank above).
Interesting question would indeed be for which bases pentation has a lower fixed point (but indeed I think this was computed already on the forum, perhaps do a search for pentation).
