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<!--   A complete "fake package" documentation   
   $Id: 3k+1.xml,v 1.1.1.1 2001/01/05 13:37:49 gap Exp $
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<!DOCTYPE Book SYSTEM "gapdoc.dtd">

<Book Name="3k+1">

<TitlePage>
  <Title>The <Package>ThreeKPlusOne</Package> Package</Title>
  <Version>Version 42</Version>
  <Author>Dummy Authör
    <Email>3kplusone@dev.null</Email>
  </Author>

  <Copyright>&copyright; 2000 The Author. <P/>
    You can do with this package what you want.<P/> Really.
  </Copyright>
</TitlePage>

<TableOfContents/>

<Body>
  <Chapter> <Heading>The <M>3k+1</M> Problem</Heading>
    <Section Label="sec:theory"> <Heading>Theory</Heading>
      Let <M>k \in \N</M> be a natural number. We consider the sequence
      <M>n(i,  k), i  \in  \N,</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 \N</M> 
      there is an <M>m \in \N</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>http://mathsrv.ku-eichstaett.de/MGF/homes/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>
gap> ThreeKPlusOneSequence(101);
"Sorry, not yet implemented. Wait for Version 84 of the package"
</Example>
        </Description>
      </ManSection>
    </Section>
  </Chapter>
</Body>

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

</Book>

