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

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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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