Simple, But Effective
The Collatz conjecture is one of the greatest enigmas in mathematics: so simple that an eight year-old can understand it but a proof or counterexample has evaded everyone. Simply start with a positive integer. If it’s even, divide it by two: if it’s odd, multiply it by three and add one. Keep applying those rules to the resulting numbers and, no matter what number you start with, the sequence will always collapse to one. Or will it? The great Hungarian number theorists, Pál Erdős, when asked about the Collatz conjecture, replied: “I don’t think that mathematics is ready for this yet.”
This simple program allows you to try it, saving yourself a few calculator keystrokes. The amazing thing about the CC, is that adjacent integers can take wildly differing numbers of steps to reach one (try 26 and 27, for instance).
Lots of videos about the CC on YouTube if you want to know more.
This simple program allows you to try it, saving yourself a few calculator keystrokes. The amazing thing about the CC, is that adjacent integers can take wildly differing numbers of steps to reach one (try 26 and 27, for instance).
Lots of videos about the CC on YouTube if you want to know more.
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