BCMATH programs for some generalized 3x+1 mapping sequences and other recursively defined integer sequences

1. The 3x+1 (Collatz) conjecture
2. The 3x+3^k (generalized-Collatz) conjecture
3. Two mappings of Keith Matthews
   • The 3x+371 (generalized-Collatz) conjecture
   • A 3-branched generalized-Collatz conjecture
   • A 6-branched generalized-Collatz conjecture
4. Two mappings of Brian Gurbaxani
5. Two mappings of David Bařina
   • A 4-branched example
   • An 8-branched example
6. Some mappings of Pruthviraj Hajari
   • Mapping 1
   • Mapping 2
   • Mapping 3
   • Mapping 4
7. Some of G. Venturini's mappings
   • Example 1 of G. Venturini
     
   • Example 4 of G. Venturini
     
   • Example 5 of G. Venturini
     
   • Example 7 of G. Venturini
     
   • Example 8 of G. Venturini
     
8. Two mappings of Mridul Sen
   • Conjecture
   • Prime conjecture
9. John Horton Conway's cycling sequence
10. 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
      
11. Mappings of Benoit Cloitre
    
12. Mapping of Kevin Lamoreau
    
13. Mappings of Tomás Oliveira e Silva
    
14. Two mappings of Felipe Gonçalves, Rachel Greenfield and Jose Madrid:
    • 4-branched mapping
    • 12-branched mapping
15. Wiggin's conjecture
16. Combining the 5x+1 and 3x+1 mappings
17. Frequency program
18. 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.
19. Finding the canonical form of Markov matrix Q_T(m) arising from George Leigh's Markov chain {Y_n(x)}