  
  [1X1. The 3k+1 Problem[0X
  
  
  [1X1.1 Theory[0X
  
  Let  k  in  N be a natural number. We consider the sequence n(i, k), i in N,
  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 N there is an m in N
  with n(m, k) = 1.
  
  [5XThreeKPlusOne[0X provides the function [2XThreeKPlusOneSequence[0X ([14X1.2-1[0X) to explore
  this  for  given n. If you really want to know something about this problem,
  see [Wir98] or [7Xhttp://mathsrv.ku-eichstaett.de/MGF/homes/wirsching/[0X for more
  details (and forget this package).
  
  
  [1X1.2 Program[0X
  
  In this section we describe the main function of this package.
  
  [1X1.2-1 ThreeKPlusOneSequence[0X
  
  [2X> ThreeKPlusOneSequence( [0X[3Xk[, max][0X[2X ) ________________________________[0Xfunction
  
  This  function computes for a natural number [3Xk[0X the beginning of the sequence
  n(i,  k)  defined  in  section  [14X1.1[0X. The sequence stops at the first 1 or at
  n([3Xmax[0X, k), if [3Xmax[0X is given.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4Xgap> ThreeKPlusOneSequence(101);[0X
    [4X"Sorry, not yet implemented. Wait for Version 84 of the package"[0X
  [4X------------------------------------------------------------------[0X
  
