3 becomes 10 becomes 5 becomes 16

  • Thread starter kmikias
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In summary, The conversation centers around the Collatz conjecture, which involves repeatedly multiplying odd numbers by 3 and adding 1, or dividing even numbers by 2, to eventually reach 1. The question is whether all numbers will eventually reach 1, or if there are some that never do. The speaker also mentions that this is a well-known problem and encourages the listener to send any proof they find to them instead of their professor.
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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.
 
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  • #2


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!
 

FAQ: 3 becomes 10 becomes 5 becomes 16

What does "3 becomes 10 becomes 5 becomes 16" mean?

This phrase is often used to describe a sequence of numbers, where each number is determined by the previous number multiplied by a certain factor and then added by a constant. In this case, the sequence would be 3, 10, 5, 16, and so on.

What is the formula for this sequence?

The formula for this sequence is n = (n-1)*3 + 1, where n represents the position of the number in the sequence. For example, the first number (3) is found by plugging in n=1, the second number (10) by plugging in n=2, and so on.

Why is the sequence sometimes referred to as the "Syracuse sequence"?

The sequence is sometimes called the "Syracuse sequence" because it was first studied by mathematician Lothar Collatz in 1937 while he was a professor at Syracuse University. It is also known as the "3n+1 problem" or the "Collatz conjecture."

Is there a pattern or trend in this sequence?

Despite being studied extensively, there has been no proof of a pattern or trend in this sequence. It is considered an open problem in mathematics and has been verified for numbers up to 5.8 x 10^18, but it is still not known if the sequence will eventually reach 1 for all starting numbers.

What are the applications of this sequence?

Although this sequence may not have any practical applications, it has sparked interest and research in number theory and dynamical systems. It has also been used as an example in computer science for testing algorithms and programming languages.

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