(HP17BII) What way for a loop stop condition ?

[Nihotte(lma)]

(HP17BII) What way for a loop stop condition ?

You know the Czech guess, of course (conjecture tchèque in French) ?

In fact, i have a question !
Just be a little patient...

A natural equation for the resolution of this sequence on the HP17BII would be as follows :

Code:


SUITE = IF(N>1 :
       IF(MOD(N:2)=0 : 
              L(N:N÷2) : 
              L(N:Nx3+1)
           ) :
       N
    )

with this use process :

[CALC] gives [SUITE] [N]

3 [N] --> N=3
[SUITE] --> SUITE=10
[SUITE] --> SUITE=5
[SUITE] --> SUITE=16
[SUITE] --> SUITE=8
[SUITE] --> SUITE=4
[SUITE] --> SUITE=2
[SUITE] --> SUITE=1

So, 3 requires 7 steps to become 1

But, if you want an easy way to follow the number of sequences from the initial N until 1, you could modify the equation as well :

Code:


SUITE = IF(N>1 :
       IF(MOD(N:2)=0 : 
              L(N:Nv2) : 
              L(N:Nx3+1)
           ) x SGN(L(NB:NB+1):
       N
    ) + NB÷1E4

with a very similar use process :

[CALC] gives [SUITE] [N] [NB]
DSP [FIX] 4 INPUT

3 [N] --> N=3.0000
[SUITE] --> SUITE=10.0001
[SUITE] --> SUITE=5.0002
[SUITE] --> SUITE=16.0003
[SUITE] --> SUITE=8.0004
[SUITE] --> SUITE=4.0005
[SUITE] --> SUITE=2.0006
[SUITE] --> SUITE=1.0007

and the same number of steps to move 3 to 1

This time, there is a satisfying equation... for a little sequence and if you have a good memory to remember the initial N !!

So, a step further, i propose you to evolve this equation by modifying it again.
Then, i use a internal variable to conserve the initial N and i do the insertion of a loop control to computerize the sequence from N to 1.

This is the equation :

Code:


CT = Σ(I : 0 : L(W:N)x0 + MAX : 1 :
       IF( G(W) > 1 : 
           IF( FP( L(W : G(W) ÷ 2)) <> 0 :
           SGN( L(W : G(W)x6 + 1) ) :
                   1
           ) :
               0
       )
      )

and the use process evolves as follow :

[CALC] gives [CT] [N] [MAX]
DSP [ALL]
10 [MAX]
3 [N]
[CT] --> CT=7

Now, you receive the number of sequence as a result of the equation with [CT].
That's OK.
What is more disputable is that :
- we need to know beforehand the maximum number of iterations to perform, before launching the evaluation of the equation
- if we have incorrectly evaluated the maximum number of iterations necessary, we will not know it
- if we choose for security a very large forecast number of iterations, the calculator will perform a very long processing without this being necessary
- to be fair, the maximum should be adjusted for each evaluation of the number of sequences with each number: compare CT(3)=7 with CT(837799)=524...

So, a new alternative to modifying the equation could be this :

Code:


CT = Σ(I : 0 : L(W:N)x0 + MAX : 1 :
       IF(W > 1 : 
           IF( FP( L(W : W ÷ 2)) <> 0 :
           SGN( L(W : Wx6 + 1) ) :
                   1
           ) :
               0
       )
      )

With the control of the variable [W], by RCL [W] at the end of the calculation, you should verify if the last term of the sequence is effectively 1.
You should initialize MAX to 1000 (1000 [MAX]) before enter N (3 [N] or 837799 [N]) and evaluate the equation by [CT].
However, the resolution time will always be the same with a fairly long time.

So, it's time for me to ask my question !!

Has anyone ever solved checking the end of the loop condition dynamically on the HP17BII or HP27S ? Or on the more recent HP17BII+ ?
Is there possible to have a end condition based on the evaluation of the last term of the sequence ?
Have you an other proposition to rewrite this equation in order to allow the dynamic resolution of this ?

(Is this possible stopping to loop as soon as the last term is 1 ?)