RogerBW's Blog

Perl Weekly Challenge 41: obscure number sequences 23 January 2020

I’ve been doing the Perl Weekly Challenges. The latest was about generating number sequences.

Part 1 is to list the attractive numbers (having a list of prime factors that itself contains a prime number of entries) that lie between 1 and 50 inclusive. I'm using my private set of rules for these challenges, which is that it's OK to use Perl5 modules as long as they solve only part of the problem (having a solution that's just a function call is no fun), but Perl6 should work with what's available in the language core (since it's so much larger).

So for Perl5:

use Math::Prime::Util qw(factor is_prime);

foreach my $c (1..50) {
  if (is_prime(scalar factor($c))) {
    print "$c\n";
  }
}

Meanwhile in Perl6 I build a list of relevant primes (and a hash of it so that I can look things up in it quickly), then factorise by trial modulo (inefficient, but with numbers this small it really doesn't matter).

my $top=50;

my @factors=grep {is-prime($_)}, (1..$top);
my %pc=map {$_ => 1}, @factors;

for (1..$top) -> $c {
  my $cc=$c;
  my $cn=0;
  my @ff=@factors;
  while ($cc != 1 && !(%pc{$c}:exists)) {
    my $l=@ff[0];
    while ($cc % @ff[0] == 0) {
      $cn++;
      $cc /= @ff[0];
    }
    shift @ff;
  }
  if (%pc{$c}:exists) {
    $cn++;
  }
  if (%pc{$cn}:exists) {
    say $c;
  }
}

Part 2 asks for the first twenty Leonardo numbers (calculated like Fibonacci numbers after the first two, but adding 1 each time, so 1, 1, 3, 5, 9, …).

my @stack;
foreach my $i (0..19) {
  if ($i<2) {
    push @stack,1;
  } else {
    push @stack,1+$stack[-1]+$stack[-2];
    shift @stack;
  }
  print $stack[-1],"\n";
}

I don't really need that shift @stack, but putting it in allows the number limit to be set as high as I like without risking running out of memory. Perl6 in this case works the same way, but using @stack[@stack.end] rather than $stack[-1].

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