BCMATH programs for some generalized 3x+1 mappings

1. The 3x+1 (Collatz) conjecture
2. Two mappings of Keith Matthews
   • The 3x+371 (generalized-Collatz) conjecture
   • A 3-branched generalized-Collatz conjecture
3. Some of G. Venturini's mappings
   • Example 1 of G. Venturini
     
   • Example 7 of G. Venturini
     
   • Example 8 of G. Venturini
     
4. Two mappings of Mridul Sen
   • Conjecture
   • Prime conjecture
5. Examples of H. Möller's mapping
   • d-branched example of Walter Carnielli
     
   • 3-branched example of Lu Pei
     
   • d-branched example of Lu Pei
     
   • b-branched example of Geoffrey Caveney
     
6. Mappings of Benoit Cloitre
   
7. Mappings of Tomás Oliveira e Silva
   
8. Cycle-finding program
9. Frequency program
10. Finding the canonical form of the Markov matrix Q_T(m) arising from generalized 3x+1 mappings , where either gcd(m_i, d )=1 for 0 ≤ i < d, or gcd(m_i, d²) = gcd(m_i, d) for 0 ≤ i < d and d divides m.
11. Finding the canonical form of Markov matrix Q_T(m) arising from George Leigh's Markov chain {Y_n(x)}