Experiments with the 3n+1 sequence

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Number Theory Topic
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Starting with the natural number n, a sequence of numbers will be computed:

Example: Input of the number 17.
17 is odd, it becomes: 3 * 17 + 1 = 52
52 is even, it becomes: 52 / 2 = 26
26 is even, it becomes 13
13 is odd, it becomes 40
40 is even, it becomes 20
20 is even, it becomes 10
10 is even, it becomes 5
5 is odd, it becomes 16
16 is even, it becomes 8
8 is even, it becomes 4
4 is even, it becomes 2
2 is even, it becomes 1

If the sequence reaches 1, then it is catched in an infinite loop: 1 becomes 4, 4 becomes 2 and 2 finally becomes 1 again.

Until now all numbers which were tested eventually ended up with 1. But there is no proof known that this will be be the case for all natural numbers. Here you can test your own numbers:

n:
number system: 10 2 3 16


Alfred.Wassermann@uni-bayreuth.de