# RogerBW's Blog

 The Weekly Challenge 148: Eban, Cardano 20 January 2022 I’ve been doing the Weekly Challenges. The latest involved various sorts of numerical search. (Note that this is open until 23 January 2022.) Task 1: Eban Numbers Write a script to generate all Eban Numbers <= 100. An Eban number is a number that has no letter 'e' in it when the number is spelled in English (American or British). So we have the sequence in the OEIS, of course. I could have written a number-to-words converter – but that's fairly standard library code, and it's not needed to solve the problem. So instead I wrote something much simpler. In Perl: ``````sub eban { my \$mx=shift; `````` Two lookup tables: a true value if there's no e in the representation of that digit, in the units place or the tens place. ("zero" doesn't count.) `````` my @units=(1,0,1,0,1,0,1,0,0,0); my @tens=(1,0,0,1,1,1,1,0,0,0,0); my @out; `````` For each digit (tens and units), check whether its word-representation is allowable. (So for 17 I'm actually testing "ten-seven".) For 100, the "first digit" is 10. 0 has to be special-cased because "zero" has an e but that doesn't prevent "thirty" from being valid. `````` foreach my \$i (0..\$mx) { if (\$tens[int(\$i/10)] && \$units[\$i%10] && \$i != 0) { push @out,\$i; } } return \@out; } `````` Task 2: Cardano Triplets Write a script to generate first 5 Cardano Triplets. A triplet of positive integers (a,b,c) is called a Cardano Triplet if it satisfies the below condition. which I won't try to include as an image, but in short: ``````cube root of (a + b * sqrt(c)) plus cube root of (a - b * sqrt(c)) = 1 `````` Extracting roots is hard computational work, and uses floating point which is just generally a bad idea. So let's not do that. There are a couple of useful rearrangements we can make: first here to get a simpler formula linking a, b and c, and further here building a parametric version. Another demonstration that spending minutes doing algebra can save milliseconds of runtime. Here's the Rust version: ``````fn cardano(ct: u32) -> Vec<[u32;3]> { let mut out: Vec<[u32;3]>=Vec::new(); let mut k=0; let mut cn=0; loop { `````` Using the parametric identity, generate values for `a` and for `b²c`. Now we just have to break down that latter number into its `b²` and `c` parts. `````` let a=3*k+2; let b2c=(k+1)*(k+1)*(8*k+5); `````` Set up a cheaty way of generating `b²` by increments. `````` let mut b=0; let mut b2=0; let mut inc=1; loop { b += 1; b2 += inc; inc += 2; `````` Now to be fair I could probably just have set `b2=b*b` each time through the loop and not taken much longer, but… eh, never mind. If `b²` is higher than `b²c` then `c` is less than 1 and we won't get any more valid solutions by increasing `b`. `````` if b2 > b2c { break; } `````` If `b²c` is evenly divisible by `b²` then `c` is an integer and we have a solution, in which case add it to the list and leave if we have enough. Otherwise, keep looping. `````` if b2c % b2 == 0 { out.push([a,b,b2c/b2]); cn += 1; if cn >= ct { break; } } } if cn >= ct { break; } k += 1; } out } `````` No floating point, no problem. Full code on github. Posted by David Malcolm at 09:26am on 21 January 2022 Looks like the URL for Eban numbers should be https://oeis.org/A006933 Posted by RogerBW at 10:03am on 21 January 2022 Fixed, thanks. I just wish I had some actual use for it. Comments on this post are now closed. If you have particular grounds for adding a late comment, comment on a more recent post quoting the URL of this one. Search 10 per page 20 per page 50 per page 100 per page Archive Tags 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s 3d printing action advent of code aeronautics aikakirja anecdote animation anime army astronomy audio audio tech aviation base commerce battletech beer boardgaming book of the week bookmonth chain of command children chris chronicle church of no redeeming virtues cold war comedy computing contemporary cornish smuggler cosmic encounter coup covid-19 crime cthulhu eternal cycling dead of winter doctor who documentary drama driving drone ecchi economics en garde espionage essen 2015 essen 2016 essen 2017 essen 2018 essen 2019 essen 2022 essen 2023 existential risk falklands war fandom fanfic fantasy feminism film firefly first world war flash point flight simulation food garmin drive gazebo genesys geocaching geodata gin gkp gurps gurps 101 gus harpoon historical history horror hugo 2014 hugo 2015 hugo 2016 hugo 2017 hugo 2018 hugo 2019 hugo 2020 hugo 2022 hugo-nebula reread in brief avoid instrumented life javascript julian simpson julie enfield kickstarter kotlin learn to play leaving earth linux liquor lovecraftiana lua mecha men with beards mpd museum music mystery naval noir non-fiction one for the brow opera parody paul temple perl perl weekly challenge photography podcast politics postscript powers prediction privacy project woolsack pyracantha python quantum rail raku ranting raspberry pi reading reading boardgames social real life restaurant reviews romance rpg a day rpgs ruby rust scala science fiction scythe second world war security shipwreck simutrans smartphone south atlantic war squaddies stationery steampunk stuarts suburbia superheroes suspense television the resistance the weekly challenge thirsty meeples thriller tin soldier torg toys trailers travel type 26 type 31 type 45 vietnam war war wargaming weather wives and sweethearts writing about writing x-wing young adult Special All book reviews, All film reviews
Produced by aikakirja v0.1