Small challenge

[J-F Garnier]

Thanks all for your interest!

As many of you found it (sometimes easily, too easily!) the formula to get the series is n^10 for n=5 to 24.

Trying to reproduce the series on a common Saturn-based calculator quickly shows that the term n^10 for n=23 is computed with an error of 1 ulp, whereas the 9835 correctly gives the right value (in the sense of closest representation of the exact value).
Congrat to Thomas and Valentin for finding the unexpected workaround n^5^2 !

Let's test more machines:

9835/9845, Series 80, HP-75: 23^10 = 4.14265112136E13 (correct value)
HP-71B, all Saturn-based machines (in approx. mode): 4.14265112137E13 (1 ulp error)
HP-35S: 23^10 = 4.14265112136E13 (back to the correct value)

The real surprise to be found was that the HP-35S is giving back the right answer for 23^10 !
I don't have a 33S to test, but I expect it to give the same value as the 35S.

I found it quite funny that old computers of the late 70 / early 80 on one side, and the poor unloved 35S on the other side,
all give a better result (for that particular case) than the whole generation of Saturn-based machines that spanned about 3 decades.

What we can learn from all this:

The implementation of the exponentiation changed between the Capricorn platform (Series 80 / 75C) and the Saturn machines (starting with the 71B).

Most of the time, the 35S math code is giving the same result as the 32SII (as surely intended), but since it's a rewrite and not a emulation, it can sometimes give slightly different (in this case better) answers.

J-F