collatz_recursive, a Python code which demonstrates recursive programming by considering the 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:
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.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
collatz_recursive is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
polpak, a Python code which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.