RogerBW's Blog

The Weekly Challenge 173: The Aesthetics of Sylvester 14 July 2022

I’ve been doing the Weekly Challenges. The latest involved more mathematical tests. (Note that this is open until 17 July 2022.)

Task 1: Esthetic Number

You are given a positive integer, $n.

Write a script to find out if the given number is Esthetic Number.

I.e. each digit differs from its predecessor by 1.

When this is touched on elsewhere, the number base seems to be important, so I wrote a base-10 wrapper. Raku:

sub esthetic10($n) {
    return esthetic($n,10);
}

sub esthetic($n0,$base) {
    my $n = $n0;

Set up previous digit and check flag.

    my $pdigit;
    my $ch = False;
    while ($n > 0) {

Extract the rightmost remaining digit of the number.

        my $digit = $n % $base;

If the check flag is set (which it won't be for the first time through the loop), compare it with the previous digit, and return false if they aren't 1 apart.

        if ($ch && abs($digit - $pdigit) != 1) {
            return False;
        }

Set the check flag, store the digit as previous digit, and divide $n for the next pass.

        $ch = True;
        $pdigit = $digit;
        $n = floor($n / $base);
    }

If all the tests passed, the number as a whole passes.

    return True;
}

The other languages are more or less the same: some of them relegate abs() to a maths library.

Task 2: Sylvester's sequence

Write a script to generate first 10 members of Sylvester's sequence.

which starts with 2, and x(n+1) is the product of x(0) to x(n), plus 1.

Which offers an optimisation, because x(n) is itself the product of all previous values plus 1, so we only need one multiplication per term:

x(n+1) = x(n) * (x(n) - 1) + 1

Since the tenth value is something like 2^346, this needs some sort of arbitrary-sized integer support. PostScript and Lua don't offer it at all (there are various third-party libraries for Lua), so I'm not writing code for them. Ruby, Python and Raku transparently use large integers as needed, and Perl can be told to. JavaScript has recently (ES2020) gained the BigInt type which just needs an "n" at the end of the literal, and can't be readily mixed with standard integers. Kotlin has BigInteger, which works similarly. And Rust has several options, but num_bigint seems to be the most widely used.

Once that's been resolved, the rest is easy. Ruby:

def sylvester(ct)
  o = [ 2 ]
  2.upto(ct) do
    o.push(1 + (o[-1] * (o[-1] - 1)))
  end
  return o
end

Full code on github.

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
Archive
Tags 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s 3d printing action 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 cycling dead of winter doctor who documentary drama driving drone ecchi economics espionage essen 2015 essen 2016 essen 2017 essen 2018 essen 2019 essen 2022 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 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 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