I recently obtained a HP80. While experimenting with various functions, I noticed that consecutive presses on (Yellow Shift)+(dot) changes the X value and the stack. Seems like doing some calculation, however couldn't find any information in the manual or elsewhere what type of function it is performing. Any idea? Thanks.
HP80 Function Question

02092012, 01:52 AM
02102012, 03:00 PM
The result is the same as SIGMA+, and there are nothing in the user's manual, if I remember well. You can make some test to verify the results in the stack: Reg X SUM of data; Reg Y Num of data; Reg Z SUM of X^2; Reg T the same of Y reg. HTH
Ignazio Edited: 10 Feb 2012, 3:02 p.m.
02102012, 04:27 PM
I was suspecting that however, after total clear:
Pressing sigma+ generates:
02102012, 07:51 PM
That's what shiftdot does on the HP80, whatever it is, starting from a clear stack:
T: 0 0 0 1 5 14 39 160 836 5192
Here is a BASIC program that produces the contents of stack registers X and Y: 5 CLS
02112012, 02:27 PM
An interesting function. I wonder if HP was thinking about another financial or statistical function which later they decided not to include thus never made it to the keyboard. I am still trying to figure out what this calculation could be used for, expecially given the numbers displayed as an integer.
02122012, 01:01 AM
Interestingly most of the first few terms are prime numbers: 1 2 3 5 11 26 66 227 1064 6257 62979 1251797 The next five terms are composites, however:
#include <iostream.h> RPL in exact mode on the HP 50g will handle those large numbers more easily than C++ though.  Update: Yes, better on the HP 50g. No more primes, however. At least up to the 30th term:
\<< 0 1 0 { } 5 ROLL 1 SWAP
Edited: 12 Feb 2012, 4:43 p.m.
02132012, 06:32 PM
Yet another implementation using Python:
def diff(xs):
I calculated the difference between sequent elements: [0, 1, 2, 3, 5, 11, 26, 66, 227, 1064] This shows that the 2nd difference is the same as the initial sequence squared and shifted.
Or as a recursive formula: This leads to the simple program:
x = [0, 1, 2] ... which produces the same result:
[0, 1, 2, 3, 5, 11, 26, 66, 227, 1064, 6257, 62979, 1251797]
I've tried in vain to use
Cheers Edited: 13 Feb 2012, 7:06 p.m.
02132012, 06:57 PM
This is my understanding what both operations sigma+ and shift dot do:
T: T + X^2 However sigma+ seems to change its mind if you don't enter a number and starts to calculate the following instead:
T: T  X^2 I filled the stack with 1:
sigma+: T: 1 2 2 18 43
shift dot: T: 1 2 6 22 71 I can't help but I think you just found a bug. Try the following:
shift CLEAR You'll get blinking 9.999999999 99 instead of 7. But you get the correct result when using shift dot instead.
Kind regards
02132012, 08:50 PM
Very nice!
Quote: It's not in OEIS either. Regards, Gerson.
02142012, 02:09 AM
Dear Thomas and Gerson,thank you very much for your responses and detailed analysis. I will use your directions and further experiment with this function. I have been away from my HP80 last couple days. I also noticed that the sequence you enter the numbers (PV first vs n first) for PMT calculation gives different results. This may be due to limited number of registers HP80 has and trying to utilize the stack as much as possible in order to solve the equation. I have feeling that shift dot is executing some sort of a subroutine which is being used as part of this solver, although it does seems like a bug since under the right conditions works better than the sigma+ function. Your responses have been very helpful, I have much more to think about now. Sincerely.
02142012, 03:09 AM
Quote: You may ask them to add it. I wonder if they'll accept it.
Since after the first step of the recursion t' = z' we can just forget about t:
Just in case somebody might not believe that two sequences are equal when they agree on the first few elements.
Cheers
Edited: 14 Feb 2012, 3:13 a.m. 
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