It is messed up how it catches your attention, isn’t it?
If I am right, and you crack the hood on it, the rules are viewing the odd numbers as the sum of one and increasing powers of two. What is determining if the odd numbers go up or down is how many powers of two there are, and how close they are. So a number like 7, with two powers of two that are sequential, (1+2^1+2^2) will end up rising (to 11), while a number like five with one power of two, or a number like 13, with two powers of two that are separated (1+2^1+2^3) will decrease. The equations showing this are at the end of the proof.
9232 being the highest number for so many has to do with how the odd number before it is represented exponentially (3077 = 1+ 2^10 + 2^11) it is a product of only two exponents, and perfectly maxed out with only one added. If you jumped up to a base odd number of 6145, or (1 + 2^11 +2^12), and multiply it by three and add one (18,436), you will have the next plateau number I would bet.
I just want to see the problem put to bed now. It feels like all this work will have been for naught if there are still people out there wasting brain power on it when they could be discovering more interesting things.
# I just want to see the problem put to bed now. It feels like all this work will have been for naught if there are still people out there wasting brain power on it when they could be discovering more interesting things.
Ya, I can see that. It’s a great thing to show to kids though. They really dig how it works. Anything that gets kids interested in math is a good thing IMO.