32 - 20 - 33

[Arnaud]

Suddenly this morning I realised something. It may not be news to you but I just wanted to share.

When I turn off my 32SII, it keeps the last result on the screen (and the whole stack for that matter.

When I turn on my 20s, it displays 0

When I turn on my 33s, in RPN or ALG mode it displays the last result (stack).

Seems an odd behaviour from the 20s. Any reason why?

Arnaud

[John Limpert]

I suppose it depends on what is defined as being part of "continuous memory". There are many old computers where the CPU registers were volatile, even though main memory was nonvolatile. Some of them had a power-fail interrupt that allowed the computer to save the contents of the registers in main memory before the power supply shut itself down.
I don't know if any calculators have a similar feature. Most modern calculators seem to have "soft" power switches instead of a hardware switch in series with the battery, like those on early calculators.

[bill platt]

Hi Arnaud,

Now that you have our attention :^)

Further interesting on the 20 is that the LAST register is saved--so if you want a result to survive power-down, just swap it into the LASTx register before power down---LASTx toggles between the calculator line and the LASTx register.

A nuance is htat when you power up again, LASTx will not toggle the "0" in and out--pressing LASTx merely fetches the same result to the calculator line.

Regards,

Bill

[Bram]

I thought I had the answer, but obviously the 33 wipes out my reasoning.

[Valentin Albillo]

Hi, Bram:

Following your posted link, I saw this question on your site:

"Properties of a number. Does the number 3.35988566622 ring a bell? In connection with Fibonacci?
You'll get this number adding the reciprocals of the elements of the Fibonacci series (the HP-32SII
program needed 56 of them to yield 11 stable decimals). It's not twice the golden ratio Phi nor have
I found any other relation between Phi and the summed value. [...] From all these ratios and reciprocals I concluded that the sum of reciprocals of the Fib series must
have a relation with Phi, but I'm still searching."

Just in case you're still searching (or interested), you'll find some interesting facts about your constant,

       3.359885666243177553172011302918927179688905133655...

at these URLs:

On-Line Encyclopedia of Integer Sequences!

MathWorld

In particular, your constant it's been proved irrational, but doesn't seem to be trivially expressible in terms of other known constants (such as Pi, e, the golden ratio, etc), so either stop searching altogether to save effort, or else persevere and should you find some representation in terms of other known constants you'll make mathematical headlines all over the world.

Menwhile, to help alleviate the frustration and for sheer fun, instead of summing the reciprocals of the Fibonacci numbers, try and find the related sum:

            n->Inf

            ------

        1   \       Fib(n)

  S =  -- *  )      ------

       10   /       10^n

            ------ 

            n = 1

where Fib(n) is the n-th Fibonacci number, like this:

   Fib(1)=1, Fib(2)=1, Fib(3)=2, Fib(4)=3, Fib(5)=5, etc. 

First obtain the value of the sum to a suitable precision, then see if you can recognize what the resulting constant is made of.

Best regards from V.

Edited: 6 Oct 2004, 12:59 p.m.

[Mike (Stgt)]

Hi!

Thank you for the links, will result in several sleeples nites <G>

Ciao.....Mike

[Bram]

Good morning Valentin,

Thanks for your comment. I happen to have hit your second link before, hence the Lucas numbers comment in the program. I should update my site on this point (and find plenty of time to read much more about it).



About the summation:

0.01

0.001

0.0002

0.00003

0.000005

0.0000008

0.00000013

0.000000021

...

add up to 0.0112359550561798...

which appears to look like the reciprocal of 89

One more number to STO in my INC. (interesting number cabinet)

[John Smitherman]

Hi Bram. I like 12/9/9 = 0.148148148.

Regards,

John