chap1.txt

  
  1 The 3k+1 Problem
  
  
  1.1 Theory
  
  Let k ∈ ℕ be a natural number. We consider the sequence n(i, k), i ∈ 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 ∈ ℕ there is an m ∈ ℕ with
  n(m, k) = 1.
  
  ThreeKPlusOne provides the function ThreeKPlusOneSequence (1.2-1) to explore
  this  for  given n. If you really want to know something about this problem,
  see                                [Wir98]                                or
  http://www.ku.de/mgf/mathematik/lehrstuhlstatistik/team/dr-guenther-wirsching/
  for more details (and forget this package).
  
  
  1.2 Program
  
  In this section we describe the main function of this package.
  
  1.2-1 ThreeKPlusOneSequence
  
  ThreeKPlusOneSequence( k[, max] )  function
  
  This  function computes for a natural number k the beginning of the sequence
  n(i,  k)  defined  in  section  1.1. The sequence stops at the first 1 or at
  n(max, k), if max is given.
  
    Example  
    gap> ThreeKPlusOneSequence(101);
    "Sorry, not yet implemented. Wait for Version 84 of the package"