Collatz conjecture

Dries vanlandschoot said:

Did some calculations and with 3×-1 i Always get 5.is this correct?

Drakkith said:

No. Starting at 6 you get the sequence above in DaveE's post.
Starting at 7 we get: 7, 20, 10, 5, 14, 7...

At first glance, the problem seems ridiculously simple. And yet experts have been searching for a solution in vain for decades. According to mathematician Jeffrey Lagarias, number theorist Shizuo Kakutani told him that during the cold war, “for about a month everybody at Yale [University] worked on it, with no result. A similar phenomenon happened when I mentioned it at the University of Chicago. A joke was made that this problem was part of a conspiracy to slow down mathematical research in the U.S.”

The Collatz conjecture—the vexing puzzle Kakutani described—is one of those supposedly simple problems that people tend to get lost in. For this reason, experienced professors often warn their ambitious students not to get bogged down in it and lose sight of their actual research.

DaveE said:

17 is interesting (slightly); it increases and then loops back to itself. And, yes, some end at 5.

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