collatz_recursive/collatz_recursive.html

<html>

  <head>
    <title>
      COLLATZ_RECURSIVE - Demonstration of Recursive Programming for the Collatz Sequence
    </title>
  </head>

  <body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">

    <h1 align = "center">
      COLLATZ_RECURSIVE <br> Demonstration of Recursive Programming for the Collatz Sequence
    </h1>

    <hr>

    <p>
      <b>COLLATZ_RECURSIVE</b>
      is a FORTRAN90 library which
      demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
    </p>

    <p>
      The rules for generation of the Collatz sequence are recursive.
      If <b>T</b> is the current entry of the sequence, (<b>T</b> is
      assumed to be a positive integer), then the next
      entry, <b>U</b> is determined as follows:
      <ol>
        <li>
          if <b>T</b> is 1, terminate the sequence;
        </li>
        <li>
          else if <b>T</b> is even, <b>U</b> = <b>T</b>/2.
        </li>
        <li>
          else (if <b>T</b> is odd and not 1), <b>U</b> = 3*<b>T</b>+1;
        </li>
      </ol>
    </p>

    <p>
      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.
    </p>

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

    <h3 align = "center">
      Licensing:
    </h3>

    <p>
      The computer code and data files described and made available on this
      web page are distributed under
      <a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
    </p>

    <h3 align = "center">
      Languages:
    </h3>

    <p>
      <b>COLLATZ_RECURSIVE</b> is available in
      <a href = "../../c_src/collatz_recursive/collatz_recursive.html">a C version</a> and
      <a href = "../../cpp_src/collatz_recursive/collatz_recursive.html">a C++ version</a> and
      <a href = "../../f_src/collatz_recursive/collatz_recursive.html">a FORTRAN90 version</a> and
      <a href = "../../m_src/collatz_recursive/collatz_recursive.html">a MATLAB version</a>.
    </p>

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f_src/polpak/polpak.html">
      POLPAK</a>,
      a FORTRAN90 library which
      evaluates a variety of mathematical functions, including
      Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials,
      and the Collatz sequence.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          Eric Weisstein,<br>
          "The Collatz Problem",<br>
          CRC Concise Encyclopedia of Mathematics,<br>
          CRC Press, 2002,<br>
          Second edition,<br>
          ISBN: 1584883472,<br>
          LC: QA5.W45.
        </li>
      </ol>
    </p>

    <h3 align = "center">
      Source Code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "collatz_recursive.f90">collatz_recursive.f90</a>, the source code.
        </li>
        <li>
          <a href = "collatz_recursive.sh">collatz_recursive.sh</a>,
          BASH commands to compile the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "collatz_recursive_prb.f90">collatz_recursive_prb.f90</a>,
          a sample calling program.
        </li>
        <li>
          <a href = "collatz_recursive_prb.sh">collatz_recursive_prb.sh</a>,
          BASH commands to compile and run the sample program.
        </li>
        <li>
          <a href = "collatz_recursive_prb_output.txt">collatz_recursive_prb_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>COLLATZ_PATH</b> uses recursion to print the path of a Collatz sequence.
        </li>
        <li>
          <b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 09 March 2012.
    </i>

    <!-- John Burkardt -->

  </body>

  <!-- Initial HTML skeleton created by HTMLINDEX. -->

</html>