3 becomes 10 becomes 5 becomes 16

  • Context: Undergrad 
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SUMMARY

The discussion centers around the Collatz conjecture, a mathematical sequence defined by a simple iterative process: for any positive integer, if the number is odd, multiply it by three and add one; if it is even, divide it by two. The sequence generated by starting with the number 3 is illustrated as 3 becomes 10, then 5, then 16, and so forth. The conjecture posits that no matter which positive integer is chosen, the sequence will eventually reach the number 1. The participants express curiosity about whether there exist any numbers that do not converge to 1.

PREREQUISITES
  • Understanding of basic integer operations (addition, multiplication, division).
  • Familiarity with mathematical conjectures and proofs.
  • Knowledge of sequences and series in mathematics.
  • Basic programming skills for simulating the Collatz sequence.
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  • Research the history and implications of the Collatz conjecture.
  • Explore algorithms for generating the Collatz sequence in Python.
  • Study existing proofs and counterexamples related to the conjecture.
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kmikias
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Hi,I have one question for you guys because I try but didn't quite work.Last week one of professor asked me a question . he asked me this.

Think of a number (a positive integer), If it's odd, muliply by three and add one. If it's even, divide by two. Repeat this proces.

like this one : 3 becomes 10 becomes 5 becomes 16 becomes 8 becomes 25 becomes ...etc

Do you always reach 1 at some point Or are there any numbers which never reach 1?

And finally I try to find this idea in the internet but I didn't get what trying to say.
 
Mathematics news on Phys.org


that's the "Collatz conjecture". If you find a proof, don't tell your professor, he will only publish it as his own and become famous- send it to me instead!
 

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