collatz_recursive

collatz_recursive, a MATLAB code which demonstrates recursive programming by considering the simple Collatz 3n+1 problem.

The rules for generation of the Collatz sequence are recursive. If T is the current entry of the sequence, (T is assumed to be a positive integer), then the next entry, U is determined as follows:

1. if T is 1, terminate the sequence;
2. else if T is even, U = T/2.
3. else (if T is odd and not 1), U = 3*T+1;

Although the Collatz sequence seems to be finite for every starting point, this has not been proved. Over the range of starting values that have been examined, a great irregularity has been observed in the number of entries in the corresponding sequence.

The Collatz sequence is also known as the "hailstone" sequence or the "3n+1" sequence.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

collatz_recursive is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

collatz, a MATLAB code which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");

collatz_recursive_test

polpak, a MATLAB code which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.

Reference:

1. Eric Weisstein,
   "The Collatz Problem",
   CRC Concise Encyclopedia of Mathematics,
   CRC Press, 2002,
   Second edition,
   ISBN: 1584883472,
   LC: QA5.W45.

Source Code:

• collatz_path.m uses recursion to print the path of a Collatz sequence.