[1XA The File [11X3k+1.xml[1X[0X Here is the complete source of the example [5XGAPDoc[0m document [11X3k+1.xml[0m discussed in Section [14X1.2[0m. [4X--------------------------- 3k+1.xml ---------------------------[0X [4X<?xml version="1.0" encoding="UTF-8"?>[0X [4X[0X [4X<!-- A complete "fake package" documentation [0X [4X $Id: 3k+1.xml,v 1.4 2007/10/04 22:02:12 gap Exp $[0X [4X-->[0X [4X[0X [4X<!DOCTYPE Book SYSTEM "gapdoc.dtd">[0X [4X[0X [4X<Book Name="3k+1">[0X [4X[0X [4X<TitlePage>[0X [4X <Title>The <Package>ThreeKPlusOne</Package> Package</Title>[0X [4X <Version>Version 42</Version>[0X [4X <Author>Dummy Authör[0X [4X <Email>3kplusone@dev.null</Email>[0X [4X </Author>[0X [4X[0X [4X <Copyright>©right; 2000 The Author. <P/>[0X [4X You can do with this package what you want.<P/> Really.[0X [4X </Copyright>[0X [4X</TitlePage>[0X [4X[0X [4X<TableOfContents/>[0X [4X[0X [4X<Body>[0X [4X <Chapter> <Heading>The <M>3k+1</M> Problem</Heading>[0X [4X <Section Label="sec:theory"> <Heading>Theory</Heading>[0X [4X Let <M>k \in &NN;</M> be a natural number. We consider the[0X [4X sequence <M>n(i, k), i \in &NN;,</M> with <M>n(1, k) = k</M> and[0X [4X else <M>n(i+1, k) = n(i, k) / 2</M> if <M>n(i, k)</M> is even[0X [4X and <M>n(i+1, k) = 3 n(i, k) + 1</M> if <M>n(i, k)</M> is odd.[0X [4X <P/> It is not known whether for any natural number <M>k \in[0X [4X &NN;</M> there is an <M>m \in &NN;</M> with <M>n(m, k) = 1</M>.[0X [4X <P/>[0X [4X <Package>ThreeKPlusOne</Package> provides the function <Ref[0X [4X Func="ThreeKPlusOneSequence"/> to explore this for given[0X [4X <M>n</M>. If you really want to know something about this[0X [4X problem, see <Cite Key="Wi98"/> or[0X [4X <URL>http://mathsrv.ku-eichstaett.de/MGF/homes/wirsching/</URL>[0X [4X for more details (and forget this package).[0X [4X </Section>[0X [4X[0X [4X <Section> <Heading>Program</Heading>[0X [4X In this section we describe the main function of this package.[0X [4X <ManSection> [0X [4X <Func Name="ThreeKPlusOneSequence" Arg="k[, max]"/>[0X [4X <Description>[0X [4X This function computes for a natural number <A>k</A> the[0X [4X beginning of the sequence <M>n(i, k)</M> defined in section[0X [4X <Ref Sect="sec:theory"/>. The sequence stops at the first[0X [4X <M>1</M> or at <M>n(<A>max</A>, k)</M>, if <A>max</A> is[0X [4X given.[0X [4X<Example>[0X [4Xgap> ThreeKPlusOneSequence(101);[0X [4X"Sorry, not yet implemented. Wait for Version 84 of the package"[0X [4X</Example>[0X [4X </Description>[0X [4X </ManSection>[0X [4X </Section>[0X [4X </Chapter>[0X [4X</Body>[0X [4X[0X [4X<Bibliography Databases="3k+1" />[0X [4X<TheIndex/>[0X [4X[0X [4X</Book>[0X [4X[0X [4X------------------------------------------------------------------[0X