(16C) Collatz conjecture

[wynen]

Starting with any positive integer, repeat the following operation

- If the number is even, divide it by two.
- If the number is odd, triple it and add one.

The conjecture is, this process will always reach the number one.

The HP16-C has the shift an rotate operations in integer modes, which are useful for this kind of programs.

Code:

f SR

is divide by 2

Code:

f SL
g LSTx
+

is multiply by 3, even in binary mode

Show the Collatz sequence:

Code:

001 43,22, C    g LBL C
002    43 34    g PSE       // Show number
003    42  b    f SR        // divide by 2
004    43 40    g x=0       // if it is zero now, it must be 1 before
005    43 21    g RTN       // finished
006 43, 6, 4    f F? 4      // if carry is set, the number was odd 
007    43 40    g x=0       // (always false) carry set 
008    22  C      GTO C     // carry not set, number was even, divide by 2 already done
009    43  C    g RCL       // carry set, restore the number
010    42  A    f SL        
011    43 36    g LSTx
012       40      +        
013        1      [1]
014       40      +         // 3*x+1
015    22  C      GTO C

Usage:
enter a positive number
GSB C

Example:
7 GSB C
shows
7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 0