Learning Adventure #10

This problem is driving me crazy. I have been reading about it, looking at theories, reading blogs, and talking to math educators who all have confirmed I've lost my mind. You will confirm this at some point as well (and that is not my hypothesis). 

I don't know why but I will figure it out at some point tonight - I have a trend. I have found a way to predict the increase in generations by two. 

55 & 54 = 110 generations 

216 & 220 (the above multipled by 4) = 112 generations 

864 & 880 (the above multipled by 4) = 114 generations 

3456 & 3520 (the above multipled by 4) = 116 generations 

and it goes on. 

I don't think this trend in and of itself has any relevence, it is the numbers 55 & 54. I just can't put my fingers on why. Has this been said already? How did I find a number that took a long time? I have not found one that has taken any time that I would consider long as of yet. I'm going to go on to part two and see what I can graph my findings to see what I "see". 

The graphing is alittle different. What I'm seeing is that my numbers go between 55 - 165 or 110. I that significant because I started with 110 generations or is this a fluke finding? Okay, Gary, I have to ask. When I researched the 3N problem I ran across a blog that eluded to the fact that you researched this problem for over a year. Is that correct? Any assistance in this finding. I see know that I've read done to the second challenge that the numbers 54 and 55 have significance. I will continue to think about this. Anyone thought about this part of the LA yet? 

Now to answer your question of "are there any three adjacent numbers that take the same long time?" 98, 99, 100 all have 23 generations. Again they share the prime numbers of 3 and 5 which is also true of 55 and 54.