collatz, a MATLAB code which computes the Collatz sequence.

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.


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


collatz is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:


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

polpak, a MATLAB 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.


  1. Martin Gardner,
    "Slither, 3X+1 and Other Curious Questions",
    Wheels, Life, and Other Mathematical Amusements,
    WH Freeman, 1983.
  2. Patrick Honner,
    "The Simple Math Problem We Still Can't Solve",
    22 September 2022.
  3. Eric Weisstein,
    "The Collatz Problem",
    CRC Concise Encyclopedia of Mathematics,
    CRC Press, 2002,
    Second edition,
    ISBN: 1584883472,
    LC: QA5.W45.

Source Code:

Last revised on 16 June 2022.