PWC168 - Perrin Prime


Here we are with TASK #1 from The Weekly Challenge #168. Enjoy!

The challenge

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.

f(13) = [2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977]

The questions

I guess that there’s no actual question to ask, as the challenge request is blunt but otherwise clear. As an example, one might think that 3, 2, 3, 2, 5, 5 might be the first items, but otherwise the Perrin prime, as defined, is just something that belongs to the sequence, with no reference to ordering. So well, duplicates are out and first can be easily seen as first from lowest value to infinity.

The solution

In time, I’ve been often fascinated to how I could design somehow complex solutions in Perl, whereas some similar solutions in C (by others, of course) were much simpler. Even in BASIC, sometimes.

I guess this stems from two factors: my tendency to over-engineer stuff, thinkig to some distant future where I might need an extension in a direction that… is not going to happen. Not in the instance of the multiverse, anyway.

Here we have such an example, in my opinion. It helps that we have Perl and Raku, where the latter is from many points of view much powerful and expressive. So it’s easier to conjure up classes, as well as leveraging on multi-methods to cope with the initial “corner” cases, getting stuff conditionally with gather/take, etc., and I eventually ended up with this:

#!/usr/bin/env raku
use v6;

class PerrinSequence {
   has @!state = [3, 0, 2];
   method get () {
      @!state.push(@!state[0] + @!state[1]);
      return @!state.shift;

multi sub MAIN (1) { put 2 }

multi sub MAIN (2) { put '2, 3' }

multi sub MAIN (3) { put '2, 3, 5' }

multi sub MAIN (Int:D $n is copy where * > 3 = 13) {
   my $ps =;
   $ps.get for 1..7;
   my @n-primes = gather while $n > 3 {
      my $candidate = $ps.get;
      next unless $;
      take $candidate;
   [2, 3, 5, |@n-primes].join(', ').put;

Oh boy how I wish it could be much simpler and elegant. Whatever.

Perl, on the other hand, does not give that stuff out of the box, so there’s not point in translating. Let’s see what we have at our disposal, and use that.

The result, I daresay, is superior this time, in pure less is more spirit:

#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';

use ntheory 'is_prime';

my $n = shift // 13;
say join ', ', perrin_primes($n);

sub perrin_primes ($n) {
   my @pps = (2, 3, 5);
   my @state = (2, 5, 5);
   while (@pps < $n) {
      push @state, my $candidate = $state[0] + $state[1];
      shift @state;
      push @pps, $candidate if is_prime($candidate);
   return @pps;

So there I got my lesson: having an amazing hammer does not mean that everything should be treated as a nail. On the other hand, sometimes using it means hitting the nail right in the head.

Stay safe!

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