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Fibonacci numbers without programming - Printable Version

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Fibonacci numbers without programming - stored - 09-20-2017 03:13 PM

Amazingly, most of simple non-scientific 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)?

RE: Fibonacci numbers without programming - Didier Lachieze - 09-20-2017 03:51 PM

With a RPN calculator you can do:
Code:
1 ENTER 1 + LASTx x<>y + LASTx x<>y + ...


RE: Fibonacci numbers without programming - stored - 09-20-2017 04:11 PM

It worked. Good solution.
Thanks you!

RE: Fibonacci numbers without programming - Dieter - 09-20-2017 05:03 PM

(09-20-2017 03:13 PM)stored Wrote:  How to do this on RPN calculators like HP 12C, HP 42S (without programming)?

On calculators with RCL-arithmetics 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

RE: Fibonacci numbers without programming - John Keith - 09-20-2017 07:41 PM

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

RE: Fibonacci numbers without programming - Gerson W. Barbosa - 09-20-2017 08:34 PM

(09-20-2017 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.

Or two, if you do DUP2 + instead.

Gerson.

RE: Fibonacci numbers without programming - Csaba Tizedes - 09-20-2017 08:55 PM

Any blind programmable CASIO:

Code:
[1][KIN][1]
Then repeat the following:
Code:
[+][x↔K1][=]

Csaba

RE: Fibonacci numbers without programming - Jim Horn - 09-20-2017 09:54 PM

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!

RE: Fibonacci numbers without programming - John Keith - 09-20-2017 10:05 PM

(09-20-2017 08:34 PM)Gerson W. Barbosa Wrote:  
(09-20-2017 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.

Or two, if you do DUP2 + instead.

Gerson.

DOH! That's what I get for posting first, thinking later. :-)

RE: Fibonacci numbers without programming - AlexFekken - 09-20-2017 10:38 PM

(09-20-2017 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 :-)

RE: Fibonacci numbers without programming - Gerson W. Barbosa - 09-20-2017 10:40 PM

(09-20-2017 10:05 PM)John Keith Wrote:  
(09-20-2017 08:34 PM)Gerson W. Barbosa Wrote:  Or two, if you do DUP2 + instead.

Gerson.

DOH! That's what I get for posting first, thinking later. :-)

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 :-)

RE: Fibonacci numbers without programming - AlexFekken - 09-20-2017 11:18 PM

(09-20-2017 09:54 PM)Jim Horn Wrote:  If you have a matrix math capable calculator, .... A one button solution!
I really like this one: so general. The difference between doing math and arithmetic :-)

RE: Fibonacci numbers without programming - Gamo - 02-17-2018 03:17 PM

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

RE: Fibonacci numbers without programming - ttw - 02-17-2018 04:49 PM

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>>

RE: Fibonacci numbers without programming - xerxes - 02-19-2018 06:29 PM

(09-20-2017 08:55 PM)Csaba Tizedes Wrote:  Any blind programmable CASIO:

Code:
[1][KIN][1]
Then repeat the following:
Code:
[+][x↔K1][=]

Csaba

A shorter solution for the FX-180P line:
Code:
1 + +
Repeat:
Code:
x↔y =


RE: Fibonacci numbers without programming - Thomas Klemm - 02-28-2024 12:19 AM

From Musings on the HP-70:

Fibonacci Sequence

Initialisation

DSP 0
CLR
STO M
1

Loop

M+
x<>y


Result

0.
1.
1.
2.
3.
5.
8.
13.
21.
34.


References


RE: Fibonacci numbers without programming - Joe Horn - 02-28-2024 12:53 AM

After setup, press Enter once to generate each subsequent Fibonacci number.

[Image: Fibo.png]