Timeline for Does the set of happy numbers have a limiting density?

8 events

when toggle format	what		by	license	comment
Nov 8, 2017 at 21:46	comment	added	Gerry Myerson		Justin Gilmer's paper was published in Integers, Volume 13, paper A48, in 2013, see math.colgate.edu/~integers/cgi-bin/get.cgi
Oct 19, 2011 at 19:11	comment	added	Pietro Majer		Then, I wonder: is there a convenient set of hypotheses on a function s: N $\to$ N that guarantees that, for any $a\in$ N, the set {x $\in$ N : $\exists m \in$ N s.t. $s^m(x)=a$ } does have a density? Say, let's keep $s(x) < x$ for large $x$; then, I guess, some condition on the relative density of the fibers $s^{-1}(x)$ vs $s^{-1}(y)$ may be useful; etc.
Oct 19, 2011 at 7:45	history	edited	Justin Gilmer	CC BY-SA 3.0	added 26 characters in body
Oct 19, 2011 at 6:04	history	edited	Justin Gilmer	CC BY-SA 3.0	added 5 characters in body
Oct 19, 2011 at 5:49	comment	added	Dave R		Thanks Justin, this is fascinating stuff. I am persuaded that a limiting density cannot exist.
Oct 19, 2011 at 5:43	vote	accept	Dave R
Oct 19, 2011 at 5:12	comment	added	Douglas Zare		I agree that it's implausible that there would be a limiting density. I'm reminded of this question: mathoverflow.net/questions/11255/….
Oct 19, 2011 at 4:56	history	answered	Justin Gilmer	CC BY-SA 3.0