Posted 17 Jul 2013 Pick any positive integer. If you pick an odd positive integer then your next picked number is 3n+1 If you pick an even number then your next picked number is n/2 Repeat with your picked numbers until you notice something interesting. 1. What interesting event happens? 2. Why is it happening? 3. Can you prove your hypothesis in number 2? 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 i picked : then picked ..... interesting 1:4 3:10 5:16 7:22 9:28 +6 every next odd 2:1 4:2 6:3 8:4 10:5 +1 every next even 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 we will end up in 1, 4, 2, 1 cycle whatever n we choose? 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 we will end up in 1, 4, 2, 1 cycle whatever n we choose? yes. now we need to answer the last two questions 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 i picked : then picked ..... interesting 1:4 3:10 5:16 7:22 9:28 +6 every next odd 2:1 4:2 6:3 8:4 10:5 +1 every next even If you keep repeating (more than a single recurssion) you should come to the same conclusion as Barcallica. 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 This is a "famous" unsolved problem. The conjecture that every positive integer eventually leads back to 1 is called the Collatz conjecture. We won't be able to prove or disprove it here, sorry 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 It has not been proved, but most mathematicians believe this sequence eventually reaches the value of unity. Thereafter it repeats 4 2 1 ...A proof would rule out two alternatives. A cycle other than 4 2 1 ... exists The sequence is unbounded. Four other cycles are known if the starting integer can be negative. Strong heuristic arguments suggest the sequence is always bounded. No other cycle has been found for starting numbers up to ~ 5x10^{18}. An interesting way to create the sequence in binary is to append a trailing "1" and add, then remove all trailing zeros. For a starting point of 7(10) = 1 1 1(2), this gives 1111111 1011010111 100010100011 11010011011 1010001011 10000 0 Share this post Link to post Share on other sites

0 Posted 18 Jul 2013 This is a "famous" unsolved problem. The conjecture that every positive integer eventually leads back to 1 is called the Collatz conjecture. We won't be able to prove or disprove it here, sorry I was hoping the fabulous minds at Brainden could pull together. Oh well. 0 Share this post Link to post Share on other sites

Posted

Pick any positive integer.

If you pick an odd positive integer then your next picked number is 3n+1

If you pick an even number then your next picked number is n/2

Repeat with your picked numbers until you notice something interesting.

1. What interesting event happens?

2. Why is it happening?

3. Can you prove your hypothesis in number 2?

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