Merge pull request #6228 from simbabque/challenge-168

challenge 168, in Perl

2 files changed, 126 insertions, 0 deletions

diff --git a/challenge-168/julien-fiegehenn/perl/ch-1.pl b/challenge-168/julien-fiegehenn/perl/ch-1.pl
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+++ b/challenge-168/julien-fiegehenn/perl/ch-1.pl
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+#!/usr/bin/perl
+use strict;
+use warnings;
+use feature 'say';
+
+# Task 1: Perrin Prime
+# Submitted by: Roger Bell_West
+# 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]
+
+sub is_prime {
+    my $n = shift;
+    return 0 if $n < 2;
+    return 1 if $n == 2;
+    return 0 if $n % 2 == 0;
+    for (my $i = 3; $i <= sqrt($n); $i += 2) {
+        return 0 if $n % $i == 0;
+    }
+    return 1;
+}
+
+sub perrin_primes {
+    my $n = shift;
+    my %primes = map { $_ => 1 } 2, 3;
+    my @perrin = (3, 0, 2);
+    my $i = 3;
+    while (keys %primes < $n) {
+        $perrin[$i] = $perrin[$i - 2] + $perrin[$i - 3];
+        if (is_prime($perrin[$i])) {
+            $primes{$perrin[$i]} = 1;
+        }
+        $i++;
+    }
+    return sort { $a <=> $b } keys %primes;
+}
+
+my @primes = perrin_primes(13);
+say "@primes";
+
+__END__
+use Test::More;
+is_deeply \@primes, [2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977];
+done_testing;
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diff --git a/challenge-168/julien-fiegehenn/perl/ch-2.pl b/challenge-168/julien-fiegehenn/perl/ch-2.pl
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+++ b/challenge-168/julien-fiegehenn/perl/ch-2.pl
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+#!/usr/bin/perl
+use strict;
+use warnings;
+use feature 'say';
+
+# Task 2: Home Prime
+# Submitted by: Mohammad S Anwar
+# You are given an integer greater than 1.
+
+# Write a script to find the home prime of the given number.
+
+# In number theory, 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.
+
+# Further information can be found on Wikipedia and OEIS.
+
+# Example
+# As given in the Wikipedia page,
+
+# HP(10) = 773, as 10 factors as 2×5 yielding HP10(1) = 25, 25 factors as 5×5 yielding HP10(2) = HP25(1) = 55, 55 = 5×11 implies HP10(3) = HP25(2) = HP55(1) = 511, and 511 = 7×73 gives HP10(4) = HP25(3) = HP55(2) = HP511(1) = 773, a prime number.
+
+# written with github copilot
+
+# calculate the prime factors of a number
+sub prime_factors {
+    my $n = shift;
+    my @factors = ();
+    my $i = 2;
+    while ($n > 1) {
+        while ($n % $i == 0) {
+            push @factors, $i;
+            $n /= $i;
+        }
+        $i++;
+    }
+    return @factors;
+}
+
+sub is_prime {
+    my $n = shift;
+    return 0 if $n < 2;
+    return 1 if $n == 2;
+    return 0 if $n % 2 == 0;
+    for (my $i = 3; $i <= sqrt($n); $i += 2) {
+        return 0 if $n % $i == 0;
+    }
+    return 1;
+}
+
+# calculate the home prime of a number
+# In number theory, 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.
+sub home_prime {
+    my $n = shift;
+
+    return $n if is_prime($n);
+    return home_prime(join '', prime_factors($n));
+}
+
+# a version of home_prime that produces debug output at every step
+sub home_prime_debug {
+    my $n = shift;
+
+    say "n = $n";
+    return $n if is_prime($n);
+    my @factors = prime_factors($n);
+    say "factors = @factors";
+    return home_prime_debug(join '', @factors);
+}
+
+__END__
+
+use Test::More;
+is_deeply [prime_factors(10)], [2, 5];
+is_deeply [prime_factors(13)], [13];
+is_deeply [prime_factors(14)], [2, 7];
+
+is home_prime(10), 773;
+is home_prime_debug(10), 773;
+done_testing;
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