Here's an integer sequence I came up with last night that doesn't seem to be in the #oeis:
1,2,4,6,3,9,12,8,10,5,15,20,16,24,18,21,14,7,28,35
I did some code on my phone in JupyterLite (https://jupyter.org/try-jupyter/lab/) to produce it, and these two images. Will wonders never cease!
If you can work out the rule, I'll be v impressed
@christianp @gregeganSF I think the rule is: you have two integers, a >= b >= 1, initially a=b=1.
At each step, you add a*b to the sequence, then change either a or b, so that the new a*b is the least such number that isn’t already in the sequence.
@christianp @gregeganSF but now I see that this rule fits for the first 16 entries, but it would put (7,1) before (7,2).
@arborelia my code tried each of (a-1,b), (a,b-1), (a,b+1), (a+1,b) in order, incrementing the 1 of none of those are free
@christianp oh and I see how this isn't the same. the rule I described would not get off the ground -- it would keep b=1 forever and just produce 1, 2, 3, 4, 5, ...
@arborelia yeah, I had a few false starts that ended up that way.
@christianp so, is it actually the smallest change to a or b that produces an a*b not in the sequence, with ties broken by smallest a*b?