<p>Here is the complete source of the example <strong class="pkg">GAPDoc</strong> document <code class="file">3k+1.xml</code> discussed in Section <a href="chap1_mj.html#X7B47AFA881BFC9DC"><span class="RefLink">1.2</span></a>.</p>
<Body>
<Chapter> <Heading>The <M>3k+1</M> Problem</Heading>
<SectionLabel="sec:theory"> <Heading>Theory</Heading>
Let <M>k \in &NN;</M> be a natural number. We consider the
sequence <M>n(i, k), i \in &NN;,</M> with <M>n(1, k) = k</M> and
else <M>n(i+1, k) = n(i, k) / 2</M> if <M>n(i, k)</M> is even
and <M>n(i+1, k) = 3 n(i, k) + 1</M> if <M>n(i, k)</M> is odd.
<P/> It is not known whether for any natural number <M>k \in
&NN;</M> there is an <M>m \in &NN;</M> with <M>n(m, k) = 1</M>.
<P/>
<Package>ThreeKPlusOne</Package> provides the function <Ref
Func="ThreeKPlusOneSequence"/> to explore this for given
<M>n</M>. If you really want to know something about this
problem, see <Cite Key="Wi98"/> or
<URL Text="this homepage">https://www.ku.de/mgf/mathematik/statistik/personen-des-lehrstuhls/prof-dr-guenther-wirsching</URL>
for more details (and forget this package).
</Section>
<Section> <Heading>Program</Heading>
In this section we describe the main function of this package.
<ManSection>
<Func Name="ThreeKPlusOneSequence" Arg="k[, max]"/>
<Description>
This function computes for a natural number <A>k</A> the
beginning of the sequence <M>n(i, k)</M> defined in section
<Ref Sect="sec:theory"/>. The sequence stops at the first
<M>1</M> or at <M>n(<A>max</A>, k)</M>, if <A>max</A> is
given.
<Example>
<span class="GAPprompt">gap></span> <span class="GAPinput">ThreeKPlusOneSequence(101);</span> "Sorry, not yet implemented. Wait for Version 84 of the package"
</Example>
</Description>
</ManSection>
</Section>
</Chapter>
</Body>
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
