A The File 3k+1.xml Here is the complete source of the example GAPDoc document 3k+1.xml discussed in Section 1.2.  3k+1.xml            The <Package>ThreeKPlusOne</Package> Package  Version 42  Dummy Authör  3kplusone@dev.null     ©right; 2000 The Author.

  You can do with this package what you want.

Really.         The 3k+1 Problem 

Theory  Let k \in &NN; be a natural number. We consider the  sequence n(i, k), i \in &NN;, with n(1, k) = k and  else n(i+1, k) = n(i, k) / 2 if n(i, k) is even  and n(i+1, k) = 3 n(i, k) + 1 if n(i, k) is odd. 

It is not known whether for any natural number k \in  &NN; there is an m \in &NN; with n(m, k) = 1. 

  ThreeKPlusOne provides the function to explore this for given  n. If you really want to know something about this  problem, see or  http://www.ku.de/mgf/mathematik/lehrstuhlstatistik/team/dr-guenther-wirsching/  for more details (and forget this package). 

  
Program  In this section we describe the main function of this package.        This function computes for a natural number k the  beginning of the sequence n(i, k) defined in section  . The sequence stops at the first  1 or at n(max, k), if max is  given.  gap> ThreeKPlusOneSequence(101); "Sorry, not yet implemented. Wait for Version 84 of the package"