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Moving one picture from the visualizations section to the lead: while the section as a whole probably still has worth, at least one picture needs to be at the top as the go-to demonstration of the rule, as one picture can help explain it so much more than words. |
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{{short description|Conjecture in mathematics that, starting with any positive integer n, if one halves it (if even) or triples it and adds one (if odd) and repeats this ad infinitum, then one eventually obtains 1}}
{{unsolved|mathematics|Does the Collatz sequence eventually reach 1 for all positive integer initial values?}}
[[File:Collatz-graph-50-no27.svg|150px|thumb|[[Directed graph]] showing the [[Orbit (dynamics)|orbits]] of small numbers under the Collatz map. The Collatz conjecture is equivalent to the statement that all paths eventually lead to 1.]]
The '''Collatz conjecture''' is a [[conjecture]] in [[mathematics]] that concerns a [[sequence]] defined as follows: start with any [[positive integer]] {{mvar|n}}. Then each term is obtained from the previous term as follows: if the previous term is [[Parity (mathematics)|even]], the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of {{mvar|n}}, the sequence will always reach 1.
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