[VA] SRC #012c - Then and Now: Sum

[Valentin Albillo]

.
Hi, FLISZT, Werner, J-F Garnier, John Keith and Fernando del Rey,

A few assorted comments to what all of you said in your posts:

FLISZT Wrote:Yes I'm ready. With the 9th Symphony of Bruckner broadcasted at the radio / Eugen Jochum / Bavarian Radio Orchestra (1954) and now the Concerto for Piano & Orch #3 / Robert Casadesus, New York Philh, Dimitri Mitropoulos (live, 1957)… how could it not be the case?!

Hehe, another classical music lover, like me. There was a time many years ago when I listened to classical music exclusively, nothing else appealed to me; it lasted for a few years, then I diversified again. By the way, I guess that your FLISZT alias honors Franz Liszt, amirite ?

FLISZT Wrote:Here is my attempt:

Very nice, thank you for going ahead and posting it here. But that is just the definition of the recursive f(n), you still need to provide the code which computes the sum ... ... and btw, thanks for editing that code panel out.

Werner Wrote:Well, I have a result.. [...] I still have to double-check my code and my reasoning ;-) Execution is pretty fast (a blink of an eye on Free42, will run it on my 42S when I'm reasonably certain it is correct)

Ok, please post your code when you see fit but do try to avoid spoiling the fun for other people working on their own solutions right now. Oh, I see you've posted it already ...

Werner Wrote:Time for my reasoning and code ;-) [...] To calculate the H(n) [...] (thanks Albert!)

Thanks a lot for your very detailed reasoning and nice HP-42S RPN code, Werner, your teaming with Albert (Chan, I suppose, who avoids posting here for whatever reason) has indeed delivered the goods: code, result, timing.

The only thing remaining is to ascertain that your result is correct, which will be most likely the case if someone else reproduces it using a wholly different program. We'll see ...

J-F Garnier Wrote:Clearly brute force is not the way to go, but I can't figure out a short-cut.

Stick to it, please, I'm sure you'll eventually manage.

John Keith Wrote:I wouldn't call f(n) an "unassuming series", [...]

(tongue in cheek) "Write a sumptuous program to summarily sum this unassuming yet serious series:"

John Keith Wrote:it's really quite a complex and interesting series. Being recursive it can take some time to compute for larger numbers [...]

Not really, unless the numbers are humongously large. For instance, f(1,000,000,000) needs only the initial call and 4 recursive calls, if I counted'em right.

John Keith Wrote:This is still basically brute force and I don't have a complete program ready yet but at least the germ of an idea.

Good. Do persevere and post your completed program when ready, please. Remember: post code (no panels), sample run, result, timing and comments if at all possible.

Fernando del Rey Wrote:I've been working on-and-off on this new problem, and can't get beyond the useless brute force approach. [...] I've tried to transform the series into an equivalent series with faster convergence, but so far I did not get anywhere. I have not given up, however[...]

Don't despair, Fernando, it's just a matter of perseverance and lo and behold, the correct "trick" comes to mind in a flash. There's still plenty of time for you to produce a correct solution before I post my original one.


Well, thanks to all of you for your interest, you still have a number of days before I post my 6-line original solution.

Best regards.
V.