RogerBW's Blog

The Weekly Challenge 168: At Home with the Perrins 09 June 2022

I’ve been doing the Weekly Challenges. The latest involved more furkling about with prime numbers. (Note that this is open until 12 June 2022.)

Task 1: Perrin Prime

The Perrin sequence is defined to start with [3, 0, 2]; after that, term N is the sum of terms N-2 and N-3. (So it continues 3, 2, 5, 5, 7, ….)

A Perrin prime is a number in the Perrin sequence which is also a prime number.

Calculate the first 13 Perrin Primes.

Perrin pseudo-primes have some interesting properties, but take a while to find – and Perl's Math::Prime::Util already has optimised code for finding them. Which is why I proposed this one instead.

There are various fiddly ways of generating arbitrary terms in the sequence, but since I want the whole sequence anyway I don't bother. The output numbers won't be in order and may have duplicates, so I store the results in a set. Ruby:

def perrinprime(n)
  out =
  seq = [3, 0, 2]
  while true do

Roll the sequence.

    seq.push(seq[0] + seq[1])

Prime-test and store.

    if seq[-1].prime? then
      if out.length >= n then
  return out.to_a.sort

(For other languages I have a primality tester from earlier challenges.)

Task 2:

You are given an integer greater than 1.

Write a script to find the home prime of the given number.

The home prime HP(n) of an integer n greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions.

In other words, to calculate HP(10) we run through:

primefactors(10) = (2, 5) → 25
primefactors(25) = (5, 5) → 55
primefactors(55) = (5, 11) → 511
primefactors(511) = (7, 73) → 773
primefactors(773) = (773)

(If I wanted a whole sequence of these, I'd build up a map as I did in task 164.2 "Happy Numbers" – all of these numbers (10, 25, 55, 511, 773) would have the same home prime of 773.)

I already have prime factorisation code from earlier challenges, so I'll re-use that. Raku:

sub homeprime($n0) {
    my $n = $n0;
    while (True) {

Get the prime factors.

        my $t = primefactor($n);

If there was only one prime factor and its exponent is 1, the result is prime; exit.

        if ($t.elems == 1 && $t.values.max() == 1) {

Otherwise, build up a string concatenation of the prime factors.

        my $ns = '';
        for ($t.keys.sort({ $^a <=> $^b })) -> $d {
            for (1..$t{$d}) {
                $ns ~= $d;

And convert it back into a number. (Other languages get this done explicitly; in Raku, Perl and Lua they just sort of slurp across as needed.)

        $n = 0 + $ns;
    return $n;

Full code on github.

See also:
The Weekly Challenge 164: Happy Palindromes

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.

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 crystal 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 2021 hugo 2022 hugo 2023 hugo 2024 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