[VA] Short & Sweet Math Challenge #25 "San Valentin's Special: Weird Math"

[Valentin Albillo]

      
Hi, all:

First of all, thanks a lot for your interest and your participation in this challenge, really much appreciated. As stated in my OP, I'll post my original solutions and extensive comments in a few days but as there's still a number of questions left unanswered so far, I'll give you all a

       Last Chance

to address and complete them before I do. This includes the following:

Concoction the First: Weird limit

      Point d is still unaddressed:  d. Can you explain the constant component of said [asymptotic] expression ?

Concoction the Second: Weird Sum

      The main question is wholly unaddressed: What's so weird about this sum ?. Perhaps a little sleuthing (i.e.: conducting some experiments) would be of help.

Concoction the Fourth: Weird Graph

      This is mostly unaddressed. In particular no program or description of the operations required to produce the graph have been posted so far and worse, no one has produced and posted the graph itself, i.e.: an actual image of it. This is the kind of functionality for which graphics calculators are intended and I included this part specifically to give HP Prime's or RPL-models' users some opportunity to show off their calculator's worthiness for this challenge.

      Also, no attempts to factorize the polynomial have been reported, either successful or unsuccessful. This is the kind of functionality for which CAD is intended. Why don't you give it a try ? Hint: It would help to answer the main question.

      Finally, as for the main question proper, What's so weird about this graph?, it's still left unanswered. Apart from its so-described "funny" appearance, there's more to the graph than it seems at first sight. Some sleuthing would surely help.

Concoction the Sixth: Weird Year

      Both RPL code and the resulting list of the years have been produced (without comments or explanation), but nearly all the questions have been left unanswered, i.e.:

• What is the "simple but highly remarkable (striking, in fact) numeric property" ?
• (a) How many years will be listed in the output ? ,
• (b) What will be the next predicted potentially catastrophic year after 2020 ?,
• (c) Should we be concerned ?

      Also, although not explicitly asked, no program has been produced to accept a given year in range and demonstrate* whether it has the required numeric property (thus, if it indeed was/might be catastrophic) or not, which would be nice as I state that my original solution does exactly this.

      * E.g.: For property "The year's number is a factorial" and year 720 you would output "720 = 1x2x3x4x5x6" demonstrating the property, while for year 721 you would ouput "721 = not a factorial"

      Finally, programs written in other than RPL would be welcome for variety and to let readers better understand what the code does and how their RPN calcs (say) would deal with the problem.


As stated, Last Chance. Thanks and best regards.  
V.