In 1937 mathematician Lother Collatz made a conjecture after playing with a simple arithmetic calculation, which goes like this: start with any positive integer, if it is even divide by 2, if it is odd multiply by 3 and add one. Then repeat. Let’s try a couple.
5, 16, 8, 4, 2, 1
11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
Try a few more. Do you always end at 1? Collatz did, so he conjectured that any starting number would end at 1, but he couldn’t prove it. It still isn’t proved. You can do an internet search to find Collatz calculators that do the arithmetic.
Stephen Wolfram just posted a paper that examines Collatz and a number of related topics. The possibilities for understanding the deep secrets of mathematics, science, and reality itself are powerful.