COLLATZ_RECURSIVE
Demonstration of Recursive Programming for the Collatz Sequence

COLLATZ_RECURSIVE is a MATLAB library 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 GNU LGPL license.

Languages:

COLLATZ_RECURSIVE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

COLLATZ_PARFOR, a MATLAB program which seeks the maximum Collatz sequence between 1 and N, running in parallel using MATLAB's "PARFOR" feature.

POLPAK, a MATLAB library 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.
• timestamp.m prints the current YMDHMS date as a time stamp.

Examples and Tests:

• collatz_recursive_test.m, calls all the tests.
• collatz_recursive_test01.m, tests collatz_path.
• collatz_recursive_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.