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HP Forum Archive 19

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Fibonacci Sequence
Message #1 Posted by Mike T. on 20 Oct 2009, 5:19 p.m.

OK,

Following an interesting discussion earlier this evening I thought it might be fun to see just how few keystrokes you would need to calculate successive terms of the Fibonacci Sequence, preferably without using any storage registers...

I doubt it I have the best solution but thought the answer I came up with demonstrated really nicely why I like my old RPN calculator so much and that it would be interesting so see what other people came up with.

Start with a one in 'x' - all other registers zero.

Mike T.

      
Re: Fibonacci Sequence
Message #2 Posted by Ken Shaw on 20 Oct 2009, 5:26 p.m.,
in response to message #1 by Mike T.

I'm assuming this is a keystroke procedure only (not a program).

In that case, I think it's just 

Enter
Enter
Roll Up
+

Then repeat, ad infinitum.

Edit: I failed to observe initially that there is no "roll up" key on most machines, including the 12C. I was surprised to realize that this also won't work on a 42S, where the keyboard up-arrow is actually BST. However, it does work on my daily calc, the 17BII, because the up-arrow key performs a RollUp. Unfortunately it is only a keystroke solution, not a program. Obviously this is not intended for RPL machines, as it depends on a revolving 4-level stack.

Edited: 21 Oct 2009, 10:23 a.m.

            
Re: Fibonacci Sequence
Message #3 Posted by Mike T. on 21 Oct 2009, 6:01 p.m.,
in response to message #2 by Ken Shaw

Very close in approach to my 'preferred' solution and it doesn't even rely on 'Last x', but since I was using an HP33C I couldn't use Roll Up...

Mike T.

      
Re: Fibonacci Sequence
Message #4 Posted by Paul Dale on 20 Oct 2009, 5:31 p.m.,
in response to message #1 by Mike T.

On an RPL machine (three command, ? keystroked):

SWAP OVER +

On a 42 (five keystrokes, two commands):

x<>y  RCL+ ST Y

Still thinking about other models....

In the 20b scientific firmware there is a generalised Fibonacci function :-)

- Pauli

            
Re: Fibonacci Sequence
Message #5 Posted by Byron Foster on 20 Oct 2009, 5:45 p.m.,
in response to message #4 by Paul Dale

Quote:
On a 42 (five keystrokes, two commands): 
x<>y  RCL+ ST Y

One command:

RCL+ ST L

Edited: 20 Oct 2009, 5:51 p.m. after one or more responses were posted

                  
Re: Fibonacci Sequence
Message #6 Posted by Paul Dale on 20 Oct 2009, 5:49 p.m.,
in response to message #5 by Byron Foster

Nice!

I'd come up with an alternating sequence of:

    STO+ ST Y
    STO+ ST X

But that isn't nearly as nice.

- Pauli

                        
Re: Fibonacci Sequence
Message #7 Posted by Byron Foster on 20 Oct 2009, 6:13 p.m.,
in response to message #6 by Paul Dale

I recently worked on this so I could try and show off the new 7 line program display mode of the 42s/Free42 in iTunes. I came up with:

01 LBL "Fibonac"
02 1
03 STO ST L
04 LBL 00
05 STOP
06 RCL+ ST L
07 GTO 00

It's not perfect because it creates the sequence 1,2,3,... instead of 1,1,2,...

                              
Re: Fibonacci Sequence
Message #8 Posted by Paul Dale on 20 Oct 2009, 6:25 p.m.,
in response to message #7 by Byron Foster

Try:

01 LBL "Fibonac"
02 0
03 STO ST L
04 1
05 LBL 00
06 STOP
07 RCL+ ST L
08 GTO 00

- Pauli

                                    
Re: Fibonacci Sequence
Message #9 Posted by Byron Foster on 20 Oct 2009, 6:33 p.m.,
in response to message #8 by Paul Dale

Yea, that's better, but I was trying to get it to fit in 7 lines.

                                          
Re: Fibonacci Sequence
Message #10 Posted by Paul Dale on 20 Oct 2009, 6:35 p.m.,
in response to message #9 by Byron Foster

Replace the "0 STO ST L" with CLSTK and you get to 7 steps :-)

- Pauli

                                                
Re: Fibonacci Sequence
Message #11 Posted by Byron Foster on 20 Oct 2009, 8:50 p.m.,
in response to message #10 by Paul Dale

How about:

0
E^X
LBL 00
STOP
RCL+ ST L
GTO 00

Initialization isn't pretty, but it's as non destructive as you can get, and it begins the sequence correctly.

            
Re: Fibonacci Sequence
Message #12 Posted by Crawl on 24 Oct 2009, 12:18 a.m.,
in response to message #4 by Paul Dale

Another 3 command RPL:

DUP ROT +

      
Fibonacci Sequence: where is Valentin Albillo?
Message #13 Posted by Vieira, Luiz C. (Brazil) on 20 Oct 2009, 6:17 p.m.,
in response to message #1 by Mike T.

Hi, all;

Amongst many others, Valentim would be one of the guys to add some valuable comments to this thread...

Cheers.

Luiz (Brazil)

Edited: 20 Oct 2009, 6:34 p.m.

      
Re: Fibonacci Sequence
Message #14 Posted by Israel Otero on 20 Oct 2009, 6:35 p.m.,
in response to message #1 by Mike T.

Hi My program for the HP-41 of the Fibonacci sequence is: 

01 0
02 1
03 LBL 00
04 X<>Y
05 ST+ Y
06 PSE
07 GTO 00
08 .END.

The advantages are that all terms are shown and is very efficient.

Edited: 20 Oct 2009, 7:26 p.m.

      
Re: Fibonacci Sequence
Message #15 Posted by Don Shepherd on 20 Oct 2009, 7:18 p.m.,
in response to message #1 by Mike T.

OK, a program on our old friend, the 12c, using no registers and 7 steps:

1
enter
+
pse
lastx
x<-->y
goto 03
            
Re: Fibonacci Sequence
Message #16 Posted by Allen on 20 Oct 2009, 7:26 p.m.,
in response to message #15 by Don Shepherd

Don- Nice work.. I love how you program the Finance Calcs!!!

            
Re: Fibonacci Sequence
Message #17 Posted by Gerson W. Barbosa on 21 Oct 2009, 7:12 a.m.,
in response to message #15 by Don Shepherd

Hi Don,

Too late for the show, anyway an alternative 12c program that produces 0,1,1,2,3,... if we don't mind clearing some registers:

01- CLEAR SIGMA
02- 1
03- x<>y
04- PSE
05- +
06- LST x
07- GTO 03

Regards,

Gerson.

            
Re: Fibonacci Sequence
Message #18 Posted by Mike T. on 21 Oct 2009, 5:53 p.m.,
in response to message #15 by Don Shepherd

Actually this exactly key sequence that I first came up with on my HP33C.

Each sucessive iteration takes just four steps/key strokes which I thought was quite efficent, but a little cumbersome to key in...

Mike T.

      
Re: Fibonacci Sequence
Message #19 Posted by Palmer O. Hanson, Jr. on 20 Oct 2009, 8:49 p.m.,
in response to message #1 by Mike T.

On a TI A.O.S. machine like the TI-59 start with 1 in the t register and 1 in the display. Then press x<>t + and see each successive term in the display after each + .

      
Re: Fibonacci Sequence
Message #20 Posted by Kiyoshi Akima on 21 Oct 2009, 12:25 p.m.,
in response to message #1 by Mike T.

LASTx
x<>y
+
That's four keystrokes on most RPN machines. On a line-addressed machine like the HP-25, the program becomes 
01 LASTx
02 x<>y
03 +
04 PAUSE
05 GTO 01
            
Re: Fibonacci Sequence
Message #21 Posted by Mike T. on 21 Oct 2009, 6:24 p.m.,
in response to message #20 by Kiyoshi Akima

After thinking about it for a little bit on my HP33C I came up with

Enter, Enter, Rdn, Rdn, +

Admittedly not the absolutly the shortest number of keystrokes but it has a certain appeal...

                  
Re: Fibonacci Sequence
Message #22 Posted by Michael Meyer on 21 Oct 2009, 8:01 p.m.,
in response to message #21 by Mike T.

I like it. Has a nice rhythm to it.

      
Giving credit where credit is due
Message #23 Posted by Palmer O. Hanson, Jr. on 23 Oct 2009, 10:11 p.m.,
in response to message #1 by Mike T.

In an earlier submission I gave a very short keyboard sequence for finding the series on an A.O.S. machine. The idea wasn't mine. I had seen it somewhere but couldn't locate it. Now I have found the original reference which is from V5N4/5P16 of TI PPC Notes:

Quote:
SHORTEST USEFUL ROUTINE - Samuel G. Allen sends me the shortest do-something-useful routine I have seen so far: 000: X<>T + PRT RST . With the t-register clear and 1 in the display, press RST R/S and it will print a listing of the Fibonacci numbers. ...
      
Re: Fibonacci Sequence
Message #24 Posted by Kiyoshi Akima on 27 Oct 2009, 1:17 p.m.,
in response to message #1 by Mike T.

If we can alter the initial stack conditions, it can be done in one step.

Set up the stack: 

5
sqrt
1
+
2
/
ENTER
ENTER
FIX 0
5
sqrt
1/x
You'll need an additional ENTER if the FIX 0 doesn't enable stack lift.

After that, press * (multiply) to see 1. Press * again to see 1. Keep going to see 2, 3, 5, 8, 13, etc.

            
Re: Fibonacci Sequence
Message #25 Posted by Mike T. on 4 Nov 2009, 5:08 p.m.,
in response to message #24 by Kiyoshi Akima

Not sure that qualifies as the shortest but it is interesting and does show just how useful the stack can be...

Mike T.

                  
Re: Fibonacci Sequence
Message #26 Posted by Michael Meyer on 4 Nov 2009, 10:32 p.m.,
in response to message #25 by Mike T.

Impressive. Most impressive. You may be an HP Jedi yet.

                  
Re: Fibonacci Sequence
Message #27 Posted by Gerson W. Barbosa on 7 Nov 2009, 6:33 a.m.,
in response to message #25 by Mike T.

Quote:
...it is interesting and does show just how useful the stack can be...

The stack is really useful: quite by accident (as almost everything I discover) I found it can be used to solve the equation

     x
   ----- = k , k > e
   ln(x)

Start by filling the stack with k then iterate 'ln *' until the answer on the display converges (somewhat slowly if k is close to e) to the second real solution.

On my HP-45:

pi
ex
ENTER
ENTER 
ENTER
ln *    (16 times)

-> 1.084423455e02

As a comparison the HP-33s solver gives 108.442345473 (initial guess = 100). Can a non-programmable algebraic calculator do this? :-)

Gerson.

                        
The answer is Yes!
Message #28 Posted by Palmer O. Hanson, Jr. on 8 Nov 2009, 1:42 p.m.,
in response to message #27 by Gerson W. Barbosa

Gerson:

You asked:

Quote:
Can a non-programmable algebraic calculator do this? :-)

The answer is yes. Try this on a TI-30:

pi INV ln STO

then do

ln x RCL =

After 16 iterations you will see 108.44235 in the display with 108.44234529 in the display register.

I suspect that this will work with any algebraic which has a memory. It works on my Sharp EL-501W where it yields 108.4423436 after twelve iterations.

Palmer

Edited: 8 Nov 2009, 1:51 p.m.

                              
Re: The answer is Yes!
Message #29 Posted by Gerson W. Barbosa on 8 Nov 2009, 2:17 p.m.,
in response to message #28 by Palmer O. Hanson, Jr.

Quote:
You asked:
Quote:
Can a non-programmable algebraic calculator do this? :-)

The answer is yes.

Thanks! Next time I'll try to solve the problem on an algebraic calculator before asking :-) By the way, long ago, for a while, I had a TI-51-III and a TI-59. Too bad the first got broken (my fault) and the latter was stolen...

Gerson.

            
Re: Fibonacci Sequence
Message #30 Posted by Ken Shaw on 5 Nov 2009, 1:01 p.m.,
in response to message #24 by Kiyoshi Akima

Very clever!

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