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<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 MATLAB 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 = "../../m_src/collatz/collatz.html">
COLLATZ</a>,
a MATLAB library which
computes and analyzes the Collatz
sequence (or "hailstone" sequence or "3n+1 sequence");
</p>
<p>
<a href = "../../m_src/collatz_parfor/collatz_parfor.html">
COLLATZ_PARFOR</a>,
a MATLAB program which
seeks the maximum Collatz sequence between 1 and N,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/polpak/polpak.html">
POLPAK</a>,
a MATLAB 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_path.m">collatz_path.m</a>
uses recursion to print the path of a Collatz sequence.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "collatz_recursive_test.m">collatz_recursive_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "collatz_recursive_test01.m">collatz_recursive_test01.m</a>,
tests collatz_path.
</li>
<li>
<a href = "collatz_recursive_test_output.txt">collatz_recursive_test_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 09 March 2012.
</i>
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</body>
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