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# Collatz conjecture

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The **Collatz conjecture** is a conjecture (an idea which many people think is likely) in mathematics. It is named after Lothar Collatz. He first proposed it in 1937.^{[1]} It is about what happens when something is done repeatedly (over and over) starting at some integer *n*:^{[1]}^{[2]}

- If
*n*is even (divisible by two),*n*is halved (divide by two = take its half). - If
*n*is odd (not divisible by two),*n*is changed to [math]3n+1[/math].

The conjecture states that if *n* is positive, *n* will always reach one.
The problem is computationally verified for all numbers below [math]2^{68}[/math].^{[3]}
Here is an example sequence:

- 9
- 28 (9 is odd, so we triple it and add one)
- 14 (28 is even; 14 is half of 28)
- 7 (14 is even, 7 is its half)
- 22 ([math]22 = 3 \times 7 + 1[/math])
- 11
- 34
- 17
- 52
- 26
- 13
- 40
- 20
- 10
- 5
- 16 (16 is a power of two, so it will lead to 1, halving each time)
- 8
- 4
- 2
- 1 (after 1 comes 4, 2, 1, 4, 2, 1, etc.)

## References

- ↑
^{1.0}^{1.1}"Collatz Problem - from Wolfram MathWorld". Mathworld.wolfram.com. http://mathworld.wolfram.com/CollatzProblem.html. Retrieved 2012-01-20. - ↑ https://www.jstor.org/pss/2044308
- ↑ D. Barina. Convergence verification of the Collatz problem.
*The Journal of Supercomputing*, 2020. DOI: 10.1007/s11227-020-03368-x