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To: zeugma

Thanks for the hour of rabbit hole.


55 posted on 03/27/2024 3:35:57 PM PDT by Tymesup
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To: Tymesup
Thanks for the hour of rabbit hole.

LOL! You're quite welcome! one of the great things about the Collatz conjecture is that it is so incredibly simple. Any child with basic math skills can do it. I have found some serious oddities within it, like how often certain numbers show up. For instance, if you run the first 1000 numbers through it, 354 of the numbers will reach 9232 as the highest number. Out of the first 10,000, you will see 9232 pop up 1579 times.

as a shortcut you could identify numbers that show up often like that, and stop work when you hit it, because you already know:
9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
Starting with the initial value of 9232, it takes 34 steps to reach unity.

Another shortcut is that if you are testing numbers in sequence, once you hit a number than is smaller than your initial number you can stop, because you know you've already tested that number

Consider yourself lucky you only lost an hour. I independently discovered most of the weird fractal charts on the wikipedia when I started scripting and graphing the results.

56 posted on 03/27/2024 9:16:11 PM PDT by zeugma (Stop deluding yourself that America is still a free country.)
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