Keith's question reminded me a bit of a very interesting sequence, http://oeis.org/A114183, which uses the two operations floor of square root and doubling. So I built a new sequence, by analogy, based on floor of log and squaring, http://oeis.org/A217727. Does every number appear? Neil On Thu, Mar 21, 2013 at 8:26 PM, Keith F. Lynch <kfl@keithlynch.net> wrote:
Years ago I noticed that if I alternate between hitting the X^2 and the ln(X) buttons on a calculator, the result neither converges nor blows up, but just wanders around, seemingly at random. What, if anything, is known about this sequence? Does it have any fixed points? Any cycles of length N for any N? What is the distribution? The mean value (after the log step) seems to be between 0.15853 and 0.15854.
With some values it will blow up. 0 will make it blow up in one step, 1 or -1 will make it blow up in two steps, sqrt(e), -sqrt(e), sqrt(1/e), and -sqrt(1/e) in three steps, etc. The number of such explosive starting values doubles with each step. Is this set of explosive starting values dense, i.e. between any two such values is there always another?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com