Definition
Definition
The Collatz Conjecture
The Collatz Conjecture
One of the most famous unsolved problems in mathematics.
June 21, 2017 - Marc Thomson
The Collatz conjecture states that repetition of a simple rule on any positive integer will eventually converge to 1. The rule is: if the number is even, divide by 2; if the number is odd, multiple by three and add 1.
Let's implement the function in the Wolfram Language, allowing the function to memorize it as it is called.
Collatz[1]:=1;Collatz[n_?EvenQ]:=Collatz[n]=Collatz[n/2]Collatz[n_?OddQ]:=Collatz[n]=Collatz[3n+1]
When called, the function will recursively evaluate until hitting 1.
Let’s test it for arbitrarily large numbers.
Collatz/@{5,222,9123,100001}
{1,1,1,1}
Now test it for all numbers up to a certain limit.
DeleteDuplicates[Collatz/@Range[5000000]]
{1}
This doesn't prove the conjecture, but it does verify it for small numbers.
Visualization
Visualization
FURTHER EXPLORATIONS
Goldbach's conjecture
Brocard's problem
AUTHORSHIP INFORMATION
Marc Thomson
6/21/17