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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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  A The File 3k+1.xml

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  Here  is  the  complete  source  of  the  example  GAPDoc  document 3k+1.xml

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  discussed in Section 1.2.

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    3k+1.xml  

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    <?xml version="1.0" encoding="UTF-8"?>

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    <!--   A complete "fake package" documentation   

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    -->

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    <!DOCTYPE Book SYSTEM "gapdoc.dtd">

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    <Book Name="3k+1">

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    <TitlePage>

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      <Title>The <Package>ThreeKPlusOne</Package> Package</Title>

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      <Version>Version 42</Version>

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      <Author>Dummy Authör

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        <Email>[email protected]</Email>

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      </Author>

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      <Copyright>&copyright; 2000 The Author. <P/>

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        You can do with this package what you want.<P/> Really.

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      </Copyright>

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    </TitlePage>

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    <TableOfContents/>

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    <Body>

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      <Chapter> <Heading>The <M>3k+1</M> Problem</Heading>

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        <Section Label="sec:theory"> <Heading>Theory</Heading>

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          Let  <M>k \in  &NN;</M> be  a  natural number.  We consider  the

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          sequence <M>n(i, k), i \in &NN;,</M> with <M>n(1, k) = k</M> and

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          else <M>n(i+1,  k) = n(i, k)  / 2</M> if <M>n(i,  k)</M> is even

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          and <M>n(i+1, k) =  3 n(i, k) + 1</M> if  <M>n(i, k)</M> is odd.

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          <P/> It  is not known  whether for  any natural number  <M>k \in

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          &NN;</M> there is an <M>m \in &NN;</M> with <M>n(m, k) = 1</M>.

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          <P/>

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          <Package>ThreeKPlusOne</Package>  provides   the  function  <Ref

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          Func="ThreeKPlusOneSequence"/>   to  explore   this  for   given

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          <M>n</M>.  If  you really  want  to  know something  about  this

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          problem, see <Cite Key="Wi98"/> or

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          <URL>http://www.ku.de/mgf/mathematik/lehrstuhlstatistik/team/dr-guenther-wirsching/</URL>

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          for more details (and forget this package).

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        </Section>

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        <Section> <Heading>Program</Heading>

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          In this section we describe the main function of this package.

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          <ManSection> 

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            <Func Name="ThreeKPlusOneSequence" Arg="k[, max]"/>

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            <Description>

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              This  function computes  for a  natural number  <A>k</A> the

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              beginning of the sequence  <M>n(i, k)</M> defined in section

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              <Ref Sect="sec:theory"/>.  The sequence  stops at  the first

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              <M>1</M>  or at  <M>n(<A>max</A>, k)</M>,  if <A>max</A>  is

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              given.

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    <Example>

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    gap> ThreeKPlusOneSequence(101);

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    "Sorry, not yet implemented. Wait for Version 84 of the package"

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    </Example>

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            </Description>

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          </ManSection>

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        </Section>

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      </Chapter>

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    </Body>

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    <Bibliography Databases="3k+1" />

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    <TheIndex/>

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    </Book>

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