It seems that the sequence given in equation 4.2 of Cohen's paper that Dan referenced might belong in the OEIS (unless it already is and I missed it). As far as I can tell, it seems to be initial values of trajectories that are (up to their limit of experimentation) disjoint. The sequence begins: 2, 5, 16, 27, 29. 1 should probably be there as the trivial case. Kerry On Thu, Apr 30, 2015 at 5:23 PM, Neil Sloane <njasloane@gmail.com> wrote:
a_2 = A007497, a_5 = A051572 will show you some initial terms.
Please augment those entries with anything you find out!
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Thu, Apr 30, 2015 at 5:33 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This paper at least has some interesting experimental facts about it:
<
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.868&rep=rep1&typ...
.
——Dan
On Apr 30, 2015, at 1:59 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Set a_k(0) = k, and a_k(n+1) = sigma(a_k(n)), where sigma(x) is the sum of the divisors of x.
My impression is that a_k grows just barely super-exponentially, with local chaos, but very smoothly overall (regardless of k).
Does anyone have any intuitions about whether a_2(n) = a_5(m) for any n, m? That is, are the forward orbits of 2 and 5 completely disjoint?
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