collatz problem
also known as "3n+1"

 


Note that numbers longer than 500 digits are not supported and computation is terminated after 25000 steps.

Input formats:

  • dec: 428623
  • hex: 0x63A72

 

Problem description:

The Collatz conjecture is an unsolved hypothesis in mathematics named after Lothar Collatz, who first proposed it in 1937.

Take any natural number n. If n is even, divide it by 2 to get n/2, if n is odd multiply it by 3 and add 1 to obtain 3n+1. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. Question is: Why? Note that via
Collatz function
this iteration can be formulated as a closed form function that can be reformulated into the holomorphic function
Collatz function
and allows to define the Collatz fractal in the complex plane.

Usage manual:

Simply type in a natural number (up to 10 digits and internally limited to 231=2.1 billion) in the above input field and click on "Compute Collatz Series" to iterate those steps. The output is also shown in binary format. If the "Reduced ouput" option is used, any even numbers (corresponding to numbers with trailing zeros in the binary representation) are not shown. Any computation will automatically truncate after 25000 iteration steps.