Fibonacci numbers without programming

09202017, 03:13 PM
Post: #1




Fibonacci numbers without programming
Amazingly, most of simple nonscientific calculators allow to produce sequence of Fibonacci numbers with only 2 key press per number:
AC 1 + = + = + = ... On HP 17b I found solutions with 6 keys per number: For init: 0 ENTER 1 ENTER Next number: SHIFT LAST + SHIFT LAST = How to do this on RPN calculators like HP 12C, HP 42S (without programming)? 

09202017, 03:51 PM
Post: #2




RE: Fibonacci numbers without programming
With a RPN calculator you can do:
Code: 1 ENTER 1 + LASTx x<>y + LASTx x<>y + ... 

09202017, 04:11 PM
Post: #3




RE: Fibonacci numbers without programming
It worked. Good solution.
Thanks you! 

09202017, 05:03 PM
(This post was last modified: 09202017 05:03 PM by Dieter.)
Post: #4




RE: Fibonacci numbers without programming
(09202017 03:13 PM)stored Wrote: How to do this on RPN calculators like HP 12C, HP 42S (without programming)? On calculators with RCLarithmetics and direct stack access (e.g. the 42s) you can do this: 1 ENTER + RCL+ ST L RCL+ ST L RCL+ ST L ... Depending on the model this may take the same four keys as the Lastx x<>y + method... or maybe less: on the WP31s and 34s it's simply [RCL] [+] [L]. Dieter 

09202017, 07:41 PM
Post: #5




RE: Fibonacci numbers without programming
On the RPL series, if you enter two 1's on the stack, the sequence OVER OVER + will fill the stack with the Fibonacci series. Three key presses if you have the PROGRAM/STACK menu active.
John 

09202017, 08:34 PM
Post: #6




RE: Fibonacci numbers without programming  
09202017, 08:55 PM
Post: #7




RE: Fibonacci numbers without programming
Any blind programmable CASIO:
Code: [1][KIN][1] Code: [+][x↔K1][=] Csaba 

09202017, 09:54 PM
Post: #8




RE: Fibonacci numbers without programming
If you have a matrix math capable calculator, fill the stack with:
[[1 1] [1 0]] and press "X" (multiply) repeatedly. A one button solution! 

09202017, 10:05 PM
Post: #9




RE: Fibonacci numbers without programming
(09202017 08:34 PM)Gerson W. Barbosa Wrote:(09202017 07:41 PM)John Keith Wrote: On the RPL series, if you enter two 1's on the stack, the sequence OVER OVER + will fill the stack with the Fibonacci series. Three key presses if you have the PROGRAM/STACK menu active. DOH! That's what I get for posting first, thinking later. :) 

09202017, 10:38 PM
Post: #10




RE: Fibonacci numbers without programming
(09202017 09:54 PM)Jim Horn Wrote: If you have a matrix math capable calculator... A one button solution! What I really like about this solution is that it does not rely at all on the coeffificents in the recursion being 1 or on the order of the recursion being only 2. That's the difference between doing math and doing arithmetic :) 

09202017, 10:40 PM
(This post was last modified: 09202017 10:46 PM by Gerson W. Barbosa.)
Post: #11




RE: Fibonacci numbers without programming
(09202017 10:05 PM)John Keith Wrote:(09202017 08:34 PM)Gerson W. Barbosa Wrote: Or two, if you do DUP2 + instead. I have many “OVER OVER” sequences permanently written in the files, like this one here (third code box in post #20). Yet DUP2 was available in my first RPL calculator, a 28S. Hopefully I’ll never forget :) 

09202017, 11:18 PM
Post: #12




RE: Fibonacci numbers without programming  
09202017, 11:53 PM
Post: #13




RE: Fibonacci numbers without programming
(09202017 05:03 PM)Dieter Wrote: On calculators with RCLarithmetics and direct stack access (e.g. the 42s) you can do this: On calculators with STO arithmetics and direct stack access  like the HP41  you may proceed as follows: Code: start sequence Without 'synthetic programming' I would enter ST+ Y X<>Y as a program (formaly it is a program, but with only two instructions it is of cause not at all) so after the start sequence you would just press R/S as often as needed. Ciao.....MIke 

02172018, 03:17 PM
Post: #14




RE: Fibonacci numbers without programming
On any HP RPN Calculator can do Fibonacci Sequence manually without the use of program.
Key this in and repeat second line below. 1 ENTER 1 ENTER RollDown RollDown + ENTER ENTER RollDown RollDown + . . . . Gamo 

02172018, 04:49 PM
Post: #15




RE: Fibonacci numbers without programming
However, with a short program, one can get any Fibonacci number by entering the index. (Except for overflow).
<< 5 Sqrt 1 + 2 / SWAP ^ 5 Sqrt / 0 RND>> 

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