From: Allan Wechsler <acwacw@gmail.com> Date: 7/3/20, 5:02 PM
Look at the logarithmic scatterplot of A001414.
Explain the feathery diagonal bands at the bottom edge. [& a couple later posts]
I want to start by saying, patterns in semi-random looking computer plots can always be artifacts of the plotting process. Sometimes not artifacts but real (but boring) phenomena aliased against pixels, bin sizes, etc. But I think the feathers are real. Hans Havermann had already done:https://oeis.org/A001414/a001414.png which is more spread out. My version... http://www.mac-guyver.com/switham/2020/07/OEIS_A001414/A001414_lin_log.png ...has white gaps in the upper black lines that I believe are artifacts. Havermann's doesn't have the same artifacts, but possibly has others. The clear upper lines are n (the primes), n/2, n/3, n/4... but there is a dark band at sqrt(n). This is a log-log plot instead of linear-log: http://www.mac-guyver.com/switham/2020/07/OEIS_A001414/A001414_log_log.png Differently interesting at the lower edge. Higher up, you can see sqrt(n), sqrt(n)/2, maybe sqrt(n)/3, but I can't convince myself there's an n^(1/3). Â --Steve