The Collatz conjecture is this: Start with any positive integer. If it is even, divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat this process over and over, and eventually you will reach 1. For example, if you start with 3, the sequence goes 3 10 5 16 8 4 2 1, completing the path in seven steps.
This conjecture has never been proven. However, it easily seen that, assuming positive integer n satisfies the conjecture, then 2n also satisfies the conjecture, since the path for 2n must start 2n, n and then follow the same path as n.
How about the following: assuming odd positive integer n satisfies the conjecture, can it be proven that 4n+1 also satisfies the conjecture? Also, is the path longer or shorter, and by how many steps?
2007-09-15
12:02:26
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7 answers
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asked by
Anonymous
in
Mathematics