Collatz conjecture: Difference between revisions

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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|upright=0.6|[[Directed graph]] showing the [[Orbit (dynamics)|orbits]] of small numbers under the Collatz map. The Collatz conjecture is equivalent to the statementstates 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.