Neil Sloane, The OEIS Foundation and Rutgers University
Rutgers Experimental Mathematics Seminar, October 5th, 2017
See part 2 at vimeo.com/237030304
I'll discuss problems from geometry, number theory, and the theory of computing.
(i) Poonen and Rubinstein famously counted the intersection points in a regular n-gon with all diagonals drawn. But what if we start with n points on a line rather than a circle? (A6561, A290447).
(ii) Mysterious things happen when you iterate arithmetic functions, for example n -> (φ(n)+σ(n))/2. Although it is hard to believe, the orbit of 270 seems to be integral and ever-increasing (A291789). John Conway recently lost a $1000 wager on the iteration of another arithmetic function (A195264).
(iii) Back in the 1930s Emil Post studied "tag systems", which in general are now known to be universal Turing machines. However, Post's simple 3-shift tag system is still open, 80 years later. In the last month there has been some progress, but this is ongoing work and the topic will be postponed until a later talk.