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 information on this web page is distributed under the MIT license.
collatz_recursive is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
collatz, a Python code which computes and analyzes the Collatz or hailstone or 3n+1 sequence);
collatz_dict, a Python code which demonstrates how the Python dict variable type can be used to efficiently record data about the Collatz iteration.
polpak, a Python code which evaluates a variety of mathematical functions, polynomials, and sequences, including Bell, Benford, Bernoulli, Bernstein, Cardan, Catalan, Charlier, Chebyshev, Collatz, Delannoy, Euler, Fibonacci, Gegenbauer, Gudermannian, Hermite, Hofstadter, Jacobi, Krawtchouk,' Laguerre, Lambert, Legendre, Lerch, Meixner, Mertens, Moebius, Motzkin, Phi, Sigma, Stirling, Tau, Tribonacci, Zernike.