Statements (40)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Ulam_conjecture
gptkb:Collatz_conjecture gptkb:Syracuse_problem |
| gptkbp:category |
dynamical system
iterative process |
| gptkbp:field |
number theory
|
| gptkbp:formedBy |
gptkb:Lothar_Collatz
1937 |
| gptkbp:generalizes |
generalized Collatz problem
kx+1 problem mx+c problem |
| gptkbp:hasApplication |
theory of computation
algorithmic complexity randomness in mathematics |
| gptkbp:hasOpenQuestion |
Are there any nontrivial cycles?
Are there divergent trajectories? Does every positive integer eventually reach 1? |
| https://www.w3.org/2000/01/rdf-schema#label |
3x+1 problem
|
| gptkbp:notableContributor |
gptkb:Terence_Tao
gptkb:John_Conway gptkb:Jeffrey_Lagarias |
| gptkbp:numberInSeries |
gptkb:OEIS:A005836
gptkb:OEIS:A006370 gptkb:OEIS:A006577 gptkb:OEIS:A008908 |
| gptkbp:referencedIn |
gptkb:Paul_Erdős
gptkb:Richard_K._Guy gptkb:Terence_Tao,_Almost_all_orbits_of_the_Collatz_map_attain_almost_bounded_values,_2019 Wikipedia: Collatz conjecture Lagarias, Jeffrey C. (editor), The Ultimate Challenge: The 3x+1 Problem, 2010 |
| gptkbp:relatedTo |
cycle detection
stopping time hailstone sequence total stopping time parity sequence |
| gptkbp:sentence |
Take any positive integer n. If n is even, divide it by 2. If n is odd, multiply it by 3 and add 1. Repeat the process. The conjecture is that no matter what number you start with, you will always eventually reach 1.
|
| gptkbp:status |
unsolved
|
| gptkbp:bfsParent |
gptkb:Collatz_conjecture
|
| gptkbp:bfsLayer |
7
|