13 files changed, 403 insertions, 76 deletions
diff --git a/challenge-168/julien-fiegehenn/perl/ch-1.pl b/challenge-168/julien-fiegehenn/perl/ch-1.pl
new file mode 100644
index 0000000000..2e331a2415
--- /dev/null
+++ b/challenge-168/julien-fiegehenn/perl/ch-1.pl
@@ -0,0 +1,48 @@
+#!/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;
+\ No newline at end of file
diff --git a/challenge-168/julien-fiegehenn/perl/ch-2.pl b/challenge-168/julien-fiegehenn/perl/ch-2.pl
new file mode 100644
index 0000000000..9e9812d039
--- /dev/null
+++ b/challenge-168/julien-fiegehenn/perl/ch-2.pl
@@ -0,0 +1,78 @@
+#!/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;
+\ No newline at end of file
diff --git a/challenge-168/lubos-kolouch/perl/ch-1.pl b/challenge-168/lubos-kolouch/perl/ch-1.pl
new file mode 100644
index 0000000000..956d2822e4
--- /dev/null
+++ b/challenge-168/lubos-kolouch/perl/ch-1.pl
@@ -0,0 +1,33 @@
+package main;
+use strict;
+use warnings;
+use Math::Prime::Util qw(is_prime);
+
+sub generate_perrin_sequence {
+    my $n               = shift;
+    my @perrin_sequence = ( 3, 0, 2 );
+
+    my %perrin_primes;
+
+    while ( scalar keys %perrin_primes < $n ) {
+        my $next_number = $perrin_sequence[-3] + $perrin_sequence[-2];
+        push @perrin_sequence, $next_number;
+        $perrin_primes{$next_number} = 1 if is_prime($next_number);
+    }
+
+    my @primes = sort { $a <=> $b } keys %perrin_primes;
+
+    return \@primes;
+}
+
+use Test::More;
+
+is_deeply(
+    generate_perrin_sequence(13),
+    [   2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193,
+        792606555396977
+    ]
+);
+
+done_testing;
+1;
diff --git a/challenge-168/lubos-kolouch/python/ch-1.py b/challenge-168/lubos-kolouch/python/ch-1.py
new file mode 100644
index 0000000000..8c8790c5dc
--- /dev/null
+++ b/challenge-168/lubos-kolouch/python/ch-1.py
@@ -0,0 +1,39 @@
+""" Challenge 168 Task 1 LK Python """
+
+from sympy import isprime
+
+
+def generate_perrin_primes(n: int) -> list:
+    """
+    Generate all primes up to n using the Perrin sequence.
+    """
+    perrin_sequence = [3, 0, 2]
+
+    perrin_primes: dict = {}
+
+    while len(perrin_primes.keys()) < n:
+
+        next_number = perrin_sequence[-3] + perrin_sequence[-2]
+        perrin_sequence.append(next_number)
+
+        if isprime(next_number):
+            perrin_primes[next_number] = True
+
+    return sorted(perrin_primes.keys())
+
+
+assert generate_perrin_primes(13) == [
+    2,
+    3,
+    5,
+    7,
+    17,
+    29,
+    277,
+    367,
+    853,
+    14197,
+    43721,
+    1442968193,
+    792606555396977,
+]
diff --git a/challenge-168/massa/raku/ch-1.raku b/challenge-168/massa/raku/ch-1.raku
new file mode 100644
index 0000000000..2fbde00b8c
--- /dev/null
+++ b/challenge-168/massa/raku/ch-1.raku
@@ -0,0 +1,2 @@
+use v6;
+(3, 0, 2, * + * + 0 * * ... *).grep(*.is-prime).unique.head(13).sort.say
diff --git a/challenge-168/massa/raku/ch-2.raku b/challenge-168/massa/raku/ch-2.raku
new file mode 100644
index 0000000000..535eaa16fa
--- /dev/null
+++ b/challenge-168/massa/raku/ch-2.raku
@@ -0,0 +1,28 @@
+use v6;
+
+my sub factors(int \x is copy) {
+  my int $possible-factor = 2;
+  gather {
+    while x > 1 {
+      if $possible-factor.is-prime && x %% $possible-factor {
+        take $possible-factor;
+        x div= $possible-factor
+      } else {
+        Nil until is-prime ++$possible-factor
+      }
+    }
+  }
+}
+
+my sub hp(int \x is copy) {
+  loop {
+    given +[~] factors x {
+      .return if .is-prime;
+      x = $_
+    }
+  }
+}
+
+sub MAIN(Int() \n where * > 1) {
+  say hp n
+}
diff --git a/challenge-168/roger-bell-west/blog.txt b/challenge-168/roger-bell-west/blog.txt
new file mode 100644
index 0000000000..aca56403ca
--- /dev/null
+++ b/challenge-168/roger-bell-west/blog.txt
@@ -0,0 +1 @@
+https://blog.firedrake.org/archive/2022/06/The_Weekly_Challenge_168__At_Home_with_the_Perrins.html
diff --git a/challenge-168/steve-g-lynn/julia/ch-1.jl b/challenge-168/steve-g-lynn/julia/ch-1.jl
new file mode 100755
index 0000000000..e58d43e005
--- /dev/null
+++ b/challenge-168/steve-g-lynn/julia/ch-1.jl
@@ -0,0 +1,29 @@
+#!/usr/bin/julia
+#-- slower than perl or raku for this task because of slow startup
+
+using Primes
+
+function perrin(n::Int64)
+	return ( ([0 1 0; 0 0 1; 1 1 0]^n)*[3;0;2] )[1];
+end
+
+savedprimes=Array{Int64}(undef,13)
+savedprimes[1]=2; savedprimes[2]=3;savedprimes[3]=5;savedprimes[4]=7
+ctr=3;
+
+for n in (6:1000)
+	perrinval=perrin(n)
+	if (isprime(perrinval) && (ctr <=13))
+		savedprimes[ctr]=perrinval
+		global ctr=ctr+1
+	end
+end
+
+print("(")
+for n in (1:13)
+	print(savedprimes[n])
+	print(" ")
+end
+print(")\n")
+
+
diff --git a/challenge-168/steve-g-lynn/julia/ch-2.jl b/challenge-168/steve-g-lynn/julia/ch-2.jl
new file mode 100755
index 0000000000..19d4c7d498
--- /dev/null
+++ b/challenge-168/steve-g-lynn/julia/ch-2.jl
@@ -0,0 +1,15 @@
+#! /usr/bin/julia
+
+using Primes
+
+function homeprime(n::Int64)
+	ncopy=n
+	while (!isprime(ncopy))
+		ncopy=parse(Int64,join(factor(Vector,ncopy)))
+	end
+	return ncopy
+end
+
+println(homeprime(16))
+#31636373
+
diff --git a/challenge-168/steve-g-lynn/perl/ch-1.pl b/challenge-168/steve-g-lynn/perl/ch-1.pl
index a8729418aa..35818da7f9 100755
--- a/challenge-168/steve-g-lynn/perl/ch-1.pl
+++ b/challenge-168/steve-g-lynn/perl/ch-1.pl
@@ -3,8 +3,11 @@
 use Math::Prime::XS qw(is_prime);
 
 local %saveprimes=();
-for (0..150) {
-	local $chk=&perrin($_);
+local @perrin=(3,0,2);
+for (1..150) {
+	local $chk=$perrin[0];
+	push @perrin, $perrin[0]+$perrin[1];
+	shift @perrin;
 	(is_prime($chk)) && ($saveprimes{$chk}=1);
 	@saveprimes==26 && last;
 }
@@ -15,45 +18,4 @@ foreach (sort{$a<=>$b} keys %saveprimes){
 }
 print ")\n";
 
-#-- subs
 
-
-sub perrin {
-	local ($n)=@_;
-	
-	if ($n==0) { return 3 }
-	else { return &postmult_302(&matpow($n)) }
-}
-
-#-- subs for fast computation of perrin number using matrix formula
-#-- see wikipedia https://en.wikipedia.org/wiki/Perrin_number
-
-#-- [0 1 0; 0 0 1; 1 1 0]^n (only need 1st row)
-sub matpow {
-	local ($n)=@_;
-	
-	if ($n==1) { return (0,1,0) }
-	else {return &postmult_010_001_110(&matpow($n-1))}
-}
-
-
-# 3x3 matrix * [0 1 0; 0 0 1; 1 1 0] (retain 1st row of product)
-sub postmult_010_001_110 {
-	# [a11 a12 a13; a21 a22 a23; a31 a32 a33]*[0 1 0; 0 0 1; 1 1 0]
-	local ($a11,$a12,$a13)=@_; #just need 1st row
-	
-	local $b11=$a13;
-	local $b12=$a11+$a13;
-	local $b13=$a12;
-
-	return ($b11,$b12,$b13) #-- return just 1st row
-}
-
-# 3x3 matrix * [3;0;2] retain 1st element of product
-sub postmult_302 {
-	local ($a11,$a12,$a13)=@_; #-- just need 1st row
-	# [a11 a12 a13; a21 a22 a23; a31 a32 a33]*[3;0;2]
-	#
-	return $a11*3+$a13*2; #-- 1st element
-
-}
diff --git a/challenge-168/steve-g-lynn/perl/ch-2.pl b/challenge-168/steve-g-lynn/perl/ch-2.pl
new file mode 100755
index 0000000000..d1f6f0aced
--- /dev/null
+++ b/challenge-168/steve-g-lynn/perl/ch-2.pl
@@ -0,0 +1,37 @@
+#!/usr/bin/perl
+
+use Math::Prime::XS qw(is_prime sieve_primes);
+
+
+print &home_prime(16),"\n";
+#-- should be 31636373 [wikipedia example]
+
+sub home_prime {
+	local ($n)=@_;
+	while (1){
+		$n=&factors($n);
+		(is_prime($n)) && last;
+	}
+	return $n;
+}
+
+
+sub factors {
+	#--return concatenated prime factors of a number n 
+	local ($n)=@_;
+	local @primes=sieve_primes($n);
+	local $retstring="";
+	
+	if (is_prime($n)){
+		return $n;
+	}
+	else {
+		foreach $prime (sort{$a<=>$b} @primes){
+			while ( ($n % $prime) == 0){
+				$n /= $prime;
+				$retstring .= $prime;
+			}
+		}
+	}
+	return $retstring;	
+}
diff --git a/challenge-168/steve-g-lynn/raku/ch-1.p6 b/challenge-168/steve-g-lynn/raku/ch-1.p6
index ace5c647e1..9610889cf2 100755
--- a/challenge-168/steve-g-lynn/raku/ch-1.p6
+++ b/challenge-168/steve-g-lynn/raku/ch-1.p6
@@ -1,8 +1,11 @@
 #!/usr/bin/raku
 
 my %saveprimes=();
+my ($p1,$p2,$p3)=(3,0,2);
 for ^Inf {
-	my $chk=perrin($_);
+	my $chk=$p1;
+	my $p4=$p1+$p2;
+	$p1=$p2; $p2=$p3;$p3=$p4;
 	(is-prime($chk)) && (%saveprimes{$chk}=1);
 	%saveprimes.elems==13 && last;
 }
@@ -10,36 +13,4 @@ for ^Inf {
 say %saveprimes.keys.sort({.Int});
 
 
-#-- subs
 
-multi sub perrin(0) {3} 
-multi sub perrin(Int $n where ($n>0)){postmult_302(matpow($n))}
-
-#-- subs for fast computation of perrin number using matrix formula
-#-- see wikipedia https://en.wikipedia.org/wiki/Perrin_number
-
-#[0 1 0; 0 0 1; 1 1 0]^n (retain 1st row)
-multi sub matpow(1){ (0,1,0) }
-multi sub matpow(Int $n where ($n>1)) { postmult_010_001_110 (matpow($n-1)) }
-
-# 3x3 matrix * [0 1 0; 0 0 1; 1 1 0] (retain 1st row of product)
-sub postmult_010_001_110 (*@inmatrix){
-	# [a11 a12 a13; a21 a22 a23; a31 a32 a33]*[0 1 0; 0 0 1; 1 1 0]
-	my ($a11,$a12,$a13)=@inmatrix; #just need 1st row
-	
-	my $b11=$a13;
-	my $b12=$a11+$a13;
-	my $b13=$a12;
-
-	return ($b11,$b12,$b13) #-- return just 1st row
-}
-
-# 3x3 matrix * [3;0;2] retain 1st element of product
-sub postmult_302 (*@inmatrix){
-	my ($a11,$a12,$a13)=@inmatrix; #-- just need 1st row
-	# [a11 a12 a13; a21 a22 a23; a31 a32 a33]*[3;0;2]
-	#
-	my $b1=$a11*3+$a13*2; #-- 1st element
-	
-	return $b1;
-}
diff --git a/challenge-168/steve-g-lynn/raku/ch-2.p6 b/challenge-168/steve-g-lynn/raku/ch-2.p6
new file mode 100755
index 0000000000..b4183fd6d3
--- /dev/null
+++ b/challenge-168/steve-g-lynn/raku/ch-2.p6
@@ -0,0 +1,84 @@
+#!/usr/bin/raku
+
+say homeprime(16);
+# 31636373
+#-- works but slow
+
+#-- sub for home prime
+
+sub homeprime(Int $n){
+	my $ncopy=$n;
+	while (1) {
+		$ncopy=factor($ncopy).Int;
+		($ncopy.is-prime) && last;
+	}
+	return $ncopy;
+}
+
+#--sub for factorizing
+
+multi sub factor (1) {1}
+
+multi sub factor (Int $n where $n > 1){
+#-- returns string concatenation of prime factors
+#	my @primes=prime_sieve($n);
+	my @primes=find_primes($n);
+	my $retstring="";
+	my $ncopy=$n;
+
+	($n.is-prime) && (return $n);	
+	
+	for @primes -> $prime {
+		while ( ($ncopy % $prime)==0) {
+			$ncopy /= $prime;
+			$retstring ~= $prime;
+		}
+	}
+	return $retstring;
+}
+
+multi sub find_primes(Int $n where $n <= 13) {
+	my @primes=(2,3,5,7,11,13);
+	my @retval=();
+	for @primes -> $prime {
+		($prime < $n) && (push @retval, $prime);
+	}
+	return (@retval.sort);
+}
+
+multi sub find_primes(Int $n where $n > 13) {
+#-- naive approach by trial factorization    
+    my @primes=(3,7,11,13);
+    
+    my $i=13;
+    
+    while ($i < $n) {
+    	#-- count only odd numbers not ending in 5. Take 4 at a time.
+        my @testarray=();
+    
+    	(($i+4) < $n) && (push @testarray, ($i+4));
+        (($i+6) < $n) && (push @testarray, ($i+6));
+        (($i+8) < $n) && (push @testarray, ($i+8));
+        (($i+10) < $n) && (push @testarray, ($i+10));
+
+        while (@testarray.elems > 0) {
+            my $testitem=shift(@testarray);
+            unless ((($testitem % 6)==1) || (($testitem % 6)==5)) {
+            #-- use the property that prime numbers above 5 are 6k+1 or 6k-1  
+            	next;
+            }
+            for @primes -> $prime {
+                ($prime > sqrt($testitem)) && last;
+                (($testitem % $prime)==0) && last;
+            }
+            push @primes, $testitem;
+        }
+        $i += 10;
+    }
+
+    splice(@primes,0,1, <2 3 5>); #-- left out 2 and 5 earlier to avoid
+    				  #   unnecessary redundant factorizing
+    return (@primes.sort);
+}
+
+