One-Line Exact CAS Fibonacci?

[Joe Horn]

In Home, generating successive members of the Fibonacci Sequence with each press of the Enter key, without using variables, is as simple as this:



However, Home is limited to 12-digit mantissas, so the above is only accurate up to 10^12.

My question is: Is it POSSIBLE to accomplish the same goal (generating successive members of the Fibonacci Sequence with each press of the Enter key, without using variables) in CAS, thereby allowing exact results > 10^12? (The above method fails in CAS because Ans(2) has a different meaning in CAS.) If possible at all, how many ways are there of doing it? If the use of variables is required, can just one variable suffice?

I found a solution that uses the undocumented command 'bloc' but it's fugly and uses two variables that must be initialized first. So I'm eager to see all your clever and non-obvious solutions. ("Just because something is obvious to you, doesn't mean it's obvious to everybody." -- Richard J. Nelson) Have fun!

N.B. Yes, Fibonacci has been discussed MANY times here before, but AFAIK never in terms of the specific goal described above, for the HP Prime.

[Didier Lachieze]

With one variable :

[Didier Lachieze]

And here is a way to generate the successive members of the Fibonacci sequence with each press of the Enter key without using variables :



The only drawback is that you get also the previous (or next) number.

[Albert Chan]

(09-01-2018 09:38 PM)Didier Lachieze Wrote:  The only drawback is that you get also the previous (or next) number.

Maybe remove the overlap, so Ans(1) returned even Fibonacci sequence, Ans(2) for odd ?

[CyberAngel]

[[1,0]]
or is it
[[1],[0]]
I can't tell because of the template - it looks like this
||1||
||0||
then
list2mat({Ans(2,1),Ans(2,1)+Ans(1,1)},1)
[ ENTER ]
[ ENTER ]

VPN
PS: What picture service should I use - all that I tried failed
*I can't remember ... Tumblr?



HP Prime Matrix

[Mark Hardman]

(09-01-2018 07:15 PM)Didier Lachieze Wrote:  With one variable :

Based on Didier's single variable solution, this shows [n, F(n)]:

a:=0
[1,1]
[((Ans(1)+1),(a+(a:=Ans(2)))]

   

[Joe Horn]

Wow, these are all cool! I didn't even know that a+(a:=Ans) was a valid statement! Yowza!

My fugly solution that uses two variables:

Setup:
a:=1
b:=1

Command line:
bloc((b:=a),(a:=b+Ans),a)

[Didier Lachieze]

(09-02-2018 03:27 AM)Joe Horn Wrote:  Command line:
bloc((b:=a),(a:=b+Ans),a)

It doesn't work, I get 2, 4, 8, 16, 32...

This works better:
bloc((a:=b+a),(b:=Ans),a)

[Joe Horn]

(09-02-2018 08:04 AM)Didier Lachieze Wrote:  

(09-02-2018 03:27 AM)Joe Horn Wrote:  Command line:
bloc((b:=a),(a:=b+Ans),a)

It doesn't work, I get 2, 4, 8, 16, 32...

This works better:
bloc((a:=b+a),(b:=Ans),a)

Oh yeah. Oops.