Oh boy, people are going to have no idea what we’re talking about. :) I’m referring to the fact I couldn’t find any references to ||2^m 3^k||=2m+3k being known except for m<=2, when there’s an easy proof that works for m<=10 (and Rawsthorne had proved enough to infer that it’s true for m<=13 if he had thought of it). And I mean, really, once I thought to actually ask the question, “can I prove this for m=3”, and then actually sit down and work on it, getting it for m=3 and then m<=10 was really straightforward...
(Background for everyone else: Here ||n||, the “complexity” of n, refers to the smallest number of 1s needed to write n using addition and multiplication; Sloane entry here. JoshuaZ and I have been doing some work on it. Actually this post brought up a very similar notion, leading JoshuaZ to ask if he actually meant integer complexity. Whether or not ||2^m 3^k||=2m+3k in general (for m,k not both zero) is unknown; we’ve managed to prove it for m<=30.)
Was this in the context of integer complexity? If so, I have no idea what obvious stopping point you are talking about.
Oh boy, people are going to have no idea what we’re talking about. :) I’m referring to the fact I couldn’t find any references to ||2^m 3^k||=2m+3k being known except for m<=2, when there’s an easy proof that works for m<=10 (and Rawsthorne had proved enough to infer that it’s true for m<=13 if he had thought of it). And I mean, really, once I thought to actually ask the question, “can I prove this for m=3”, and then actually sit down and work on it, getting it for m=3 and then m<=10 was really straightforward...
(Background for everyone else: Here ||n||, the “complexity” of n, refers to the smallest number of 1s needed to write n using addition and multiplication; Sloane entry here. JoshuaZ and I have been doing some work on it. Actually this post brought up a very similar notion, leading JoshuaZ to ask if he actually meant integer complexity. Whether or not ||2^m 3^k||=2m+3k in general (for m,k not both zero) is unknown; we’ve managed to prove it for m<=30.)