Merge remote-tracking branch 'upstream/master'

45 files changed, 2495 insertions, 238 deletions

diff --git a/challenge-169/2colours/raku/ch-1.raku b/challenge-169/2colours/raku/ch-1.raku
new file mode 100755
index 0000000000..a17ab34df7
--- /dev/null
+++ b/challenge-169/2colours/raku/ch-1.raku
@@ -0,0 +1,19 @@
+#!/usr/bin/env raku
+
+
+my @primes = grep &is-prime, ^Inf;
+my @primes-digited = @primes.map( -> $current {                         
+  state @buffer;                                                              
+  when @buffer[0] andthen .chars == $current.chars {                          
+    @buffer.append: $current;                                                   
+    Empty                                                                       
+  }                                                                           
+  my @res = @buffer;                                                          
+  @buffer = [$current];                                                       
+  @res                                                                        
+});
+@primes-digited .= skip;
+@primes-digited.map({ ([\,] @$_) >>*>> @$_ andthen .flat.sort.Slip })
+  andthen .head: 20
+  andthen .join: ', '
+  andthen .say;
diff --git a/challenge-169/2colours/raku/ch-2.raku b/challenge-169/2colours/raku/ch-2.raku
new file mode 100755
index 0000000000..1fa0bc027d
--- /dev/null
+++ b/challenge-169/2colours/raku/ch-2.raku
@@ -0,0 +1,20 @@
+#!/usr/bin/env raku
+
+sub is-achilles($num) {
+  (powerful-exponent($num) // 0) == 1
+}
+
+multi powerful-exponent(1 --> 0) {}
+multi powerful-exponent($ where *.is-prime --> Nil) {}
+multi powerful-exponent($num) {
+  my $first-divisor = (2 .. *).first: $num %% *;
+  my $first-exponent = (1 .. *).toggle($num %% $first-divisor ** *).tail;
+  return Nil if $first-exponent == 1;
+  return $first-exponent gcd $_ with powerful-exponent($num div $first-divisor ** $first-exponent);
+  Nil
+}
+
+(1 .. *).grep: &is-achilles
+  andthen .head: 20
+  andthen .join: ', '
+  andthen .say;
\ No newline at end of file
diff --git a/challenge-169/adam-russell/blog.txt b/challenge-169/adam-russell/blog.txt
new file mode 100644
index 0000000000..20b7acb63a
--- /dev/null
+++ b/challenge-169/adam-russell/blog.txt
@@ -0,0 +1 @@
+http://www.rabbitfarm.com/cgi-bin/blosxom/perl/2022/06/19
\ No newline at end of file
diff --git a/challenge-169/adam-russell/blog1.txt b/challenge-169/adam-russell/blog1.txt
new file mode 100644
index 0000000000..5b466f5717
--- /dev/null
+++ b/challenge-169/adam-russell/blog1.txt
@@ -0,0 +1 @@
+http://www.rabbitfarm.com/cgi-bin/blosxom/prolog/2022/06/19
\ No newline at end of file
diff --git a/challenge-169/adam-russell/java/ch-1.java b/challenge-169/adam-russell/java/ch-1.java
new file mode 100644
index 0000000000..09cdd62612
--- /dev/null
+++ b/challenge-169/adam-russell/java/ch-1.java
@@ -0,0 +1,44 @@
+import java.util.ArrayList;
+
+class Brilliant{
+    private static ArrayList primeFactors(long n){
+        ArrayList factors = new ArrayList();    
+        while (n % 2 == 0){
+            factors.add(new Long(2));
+            n = n / 2;
+        }
+        for(long i = 3; i <= Math.sqrt(n); i = i + 2){
+            while (n % i == 0){
+                factors.add(new Long(i));
+                n = n / i;
+            }
+        }
+        if(n > 2)
+            factors.add(new Long(n));
+        return factors;  
+    }
+    
+    private static boolean isBrilliant(int n){
+        ArrayList factors = primeFactors(n);
+        return factors.size() == 2 && ((Long)factors.get(0)).toString().length() == ((Long)factors.get(1)).toString().length();
+    }
+    
+    public static ArrayList nBrilliants(int n){
+        ArrayList brilliants = new ArrayList();
+        int i = 0;
+        do{
+            i++;
+            if(isBrilliant(i))
+                brilliants.add(new Integer(i));
+        }while(brilliants.size() < n);
+        return brilliants;
+    }
+
+    public static void main(String[] args){        
+        ArrayList brilliants = Brilliant.nBrilliants(20);
+        for(int i = 0; i < brilliants.size() - 1; i++){
+            System.out.print(brilliants.get(i) + ", ");
+        }
+        System.out.println(brilliants.get(brilliants.size() - 1));
+    }
+}
\ No newline at end of file
diff --git a/challenge-169/adam-russell/java/ch-2.java b/challenge-169/adam-russell/java/ch-2.java
new file mode 100644
index 0000000000..47c8d7813e
--- /dev/null
+++ b/challenge-169/adam-russell/java/ch-2.java
@@ -0,0 +1,54 @@
+import java.util.ArrayList;
+
+class Achilles{
+    private static final double EPSILON = 1e-15;
+    private static ArrayList primeFactors(long n){
+        ArrayList factors = new ArrayList();    
+        while (n % 2 == 0){
+            factors.add(new Long(2));
+            n = n / 2;
+        }
+        for(long i = 3; i <= Math.sqrt(n); i = i + 2){
+            while (n % i == 0){
+                factors.add(new Long(i));
+                n = n / i;
+            }
+        }
+        if(n > 2)
+            factors.add(new Long(n));
+        return factors;  
+    }
+    
+    private static boolean isAchilles(int n){
+        ArrayList factors = primeFactors(n);
+        for(int i = 0; i < factors.size(); i++){
+            if(n % Math.pow(((Long)factors.get(i)).longValue() + 0.0, 2) != 0)
+                return false;
+        }
+        for(int i = 2; i <= Math.sqrt(n); i++) {
+            double d = Math.log(n) / Math.log(i);
+            if(Math.abs(d - Math.round(d)) < EPSILON)
+                return false; 
+        }
+        return true;
+    }
+    
+    public static ArrayList nAchilles(int n){
+        ArrayList achilles = new ArrayList();
+        int i = 1;
+        do{
+            i++;
+            if(isAchilles(i))
+                achilles.add(new Integer(i));
+        }while(achilles.size() < n);
+        return achilles;
+    }
+
+    public static void main(String[] args){        
+        ArrayList achilles = Achilles.nAchilles(20);
+        for(int i = 0; i < achilles.size() - 1; i++){
+            System.out.print(achilles.get(i) + ", ");
+        }
+        System.out.println(achilles.get(achilles.size() - 1));
+    }
+}
\ No newline at end of file
diff --git a/challenge-169/adam-russell/perl/ch-1.pl b/challenge-169/adam-russell/perl/ch-1.pl
new file mode 100644
index 0000000000..4f7367e9d2
--- /dev/null
+++ b/challenge-169/adam-russell/perl/ch-1.pl
@@ -0,0 +1,38 @@
+use strict;
+use warnings;
+##
+# Write a script to generate the first 20 Brilliant Numbers.
+##
+sub prime_factor{
+    my $x = shift(@_); 
+    my @factors;    
+    for (my $y = 2; $y <= $x; $y++){
+        next if $x % $y;
+        $x /= $y;
+        push @factors, $y;
+        redo;
+    }
+    return @factors;  
+}
+
+sub is_brilliant{
+    my($n) = @_;
+    my @factors = prime_factor($n); 
+    return @factors == 2 && length($factors[0]) == length($factors[1]);
+}
+
+sub n_brilliants{
+    my($n) = @_;
+    my @brilliants;
+    my $i = 0;
+    {
+       push @brilliants, $i if is_brilliant($i);
+       $i++;
+       redo if @brilliants < $n;
+    }
+    return @brilliants;
+}
+
+MAIN:{
+    print join(", ", n_brilliants(20)) . "\n";
+}
\ No newline at end of file
diff --git a/challenge-169/adam-russell/perl/ch-2.pl b/challenge-169/adam-russell/perl/ch-2.pl
new file mode 100644
index 0000000000..d677bc6c27
--- /dev/null
+++ b/challenge-169/adam-russell/perl/ch-2.pl
@@ -0,0 +1,48 @@
+use strict;
+use warnings;
+##
+# Write a script to generate the first 20 Achilles Numbers.
+##
+use POSIX;
+use boolean;
+
+sub prime_factor{
+    my $x = shift(@_); 
+    my @factors;    
+    for (my $y = 2; $y <= $x; $y++){
+        next if $x % $y;
+        $x /= $y;
+        push @factors, $y;
+        redo;
+    }
+    return @factors;  
+}
+
+sub is_achilles{
+    my($n) = @_;
+    my @factors = prime_factor($n); 
+    for my $factor (@factors){
+        return false if $n % ($factor * $factor) != 0;
+    }
+    for(my $i = 2; $i <= sqrt($n); $i++) {
+        my $d = log($n) / log($i) . "";
+        return false if ceil($d) == floor($d);  
+    }
+    return true;
+}
+
+sub n_achilles{
+    my($n) = @_;
+    my @achilles;
+    my $i = 1;
+    {
+       $i++;
+       push @achilles, $i if is_achilles($i);
+       redo if @achilles < $n;
+    }
+    return @achilles;
+}
+
+MAIN:{
+    print join(", ", n_achilles(20)) . "\n";
+}
\ No newline at end of file
diff --git a/challenge-169/adam-russell/prolog/ch-1.p b/challenge-169/adam-russell/prolog/ch-1.p
new file mode 100644
index 0000000000..e360089652
--- /dev/null
+++ b/challenge-169/adam-russell/prolog/ch-1.p
@@ -0,0 +1,40 @@
+prime_factors(N, L):- 
+    N > 0,  
+    prime_factors(N, L, 2).
+prime_factors(1, [], _):- 
+    !.
+prime_factors(N, [F|L], F):-                     
+    R is N // F, 
+    N =:= R * F, 
+    !, 
+    prime_factors(R, L, F).
+prime_factors(N, L, F):-
+    next_factor(N, F, NF), 
+    prime_factors(N, L, NF).
+next_factor(_, 2, 3):- 
+    !.
+next_factor(N, F, NF):- 
+    F * F < N, 
+    !, 
+    NF is F + 2.
+next_factor(N, _, N).
+
+brilliants(_) --> [].
+brilliants(Seen) --> [X], {brilliant(X), \+ member(X, Seen)}, brilliants([X|Seen]).
+
+brilliant(X):-
+    current_prolog_flag(max_integer, MAX_INTEGER),
+    between(1, MAX_INTEGER, X),
+    prime_factors(X, Factors),
+    length(Factors, 2),
+    nth(1, Factors, First),
+    nth(2, Factors, Second),
+    number_chars(First, FirstChars),
+    number_chars(Second, SecondChars),
+    length(FirstChars, FirstCharsLength),
+    length(SecondChars, SecondCharsLength),
+    FirstCharsLength == SecondCharsLength.
+
+n_brilliants(N, Brilliants):-
+    length(Brilliants, N), 
+    phrase(brilliants([]), Brilliants). 
\ No newline at end of file
diff --git a/challenge-169/adam-russell/prolog/ch-2.p b/challenge-169/adam-russell/prolog/ch-2.p
new file mode 100644
index 0000000000..7d7a8585b1
--- /dev/null
+++ b/challenge-169/adam-russell/prolog/ch-2.p
@@ -0,0 +1,51 @@
+prime_factors(N, L):- 
+    N > 0,  
+    prime_factors(N, L, 2).
+prime_factors(1, [], _):- 
+    !.
+prime_factors(N, [F|L], F):-                     
+    R is N // F, 
+    N =:= R * F, 
+    !, 
+    prime_factors(R, L, F).
+prime_factors(N, L, F):-
+    next_factor(N, F, NF), 
+    prime_factors(N, L, NF).
+next_factor(_, 2, 3):- 
+    !.
+next_factor(N, F, NF):- 
+    F * F < N, 
+    !, 
+    NF is F + 2.
+next_factor(N, _, N).
+
+powerful(N, X):-
+    M is mod(N, X * X),
+    M == 0.
+
+imperfect(N):-
+    Sqrt is round(sqrt(N)),
+    S is Sqrt - 1,
+    length(I, S),
+    fd_domain(I, 2, Sqrt),
+    fd_all_different(I),
+    fd_labeling(I),!,
+    maplist(imperfect(N), I).
+imperfect(N, X):-
+    D is log(N) / log(X),
+    Check is abs(D - round(D)),
+    \+ Check < 0.000001.
+
+achilles(_) --> [].
+achilles(Seen) --> [X], {current_prolog_flag(max_integer, MAX_INTEGER), 
+                         between(2, MAX_INTEGER, X), \+ member(X, Seen), achilles(X)}, 
+                   achilles([X|Seen]).
+
+achilles(X):-
+    prime_factors(X, Factors), 
+    maplist(powerful(X), Factors),
+    imperfect(X).
+
+n_achilles(N, Achilles):-
+    length(Achilles, N), 
+    phrase(achilles([]), Achilles). 
\ No newline at end of file
diff --git a/challenge-169/arne-sommer/blog.txt b/challenge-169/arne-sommer/blog.txt
new file mode 100644
index 0000000000..b6072b4829
--- /dev/null
+++ b/challenge-169/arne-sommer/blog.txt
@@ -0,0 +1 @@
+https://raku-musings.com/ambundance-numbers.html
diff --git a/challenge-169/arne-sommer/perl/achilles-numbers-perl b/challenge-169/arne-sommer/perl/achilles-numbers-perl
new file mode 100755
index 0000000000..1a4c199378
--- /dev/null
+++ b/challenge-169/arne-sommer/perl/achilles-numbers-perl
@@ -0,0 +1,105 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+no warnings 'experimental::signatures';
+
+use Math::Prime::Util 'is_prime';
+
+my $count = shift(@ARGV) || 20;
+
+die "Please specify a positive integer" unless $count =~ /^[1-9]\d*$/;
+
+my @achilles = ();
+
+my $candidate = 0;
+
+while (@achilles != $count)
+{
+  $candidate++;
+
+  push(@achilles, $candidate) if is_achilles($candidate);
+}
+
+say join(", ", @achilles);
+
+sub factors ($number)
+{
+  return (1)       if $number == 1;
+  return ($number) if is_prime($number);
+
+  my @factors;
+
+  for my $candidate (grep { is_prime($_) } 2 .. $number / 2)
+  {
+    while ($number % $candidate == 0)
+    {
+      push(@factors, $candidate);
+      $number /= $candidate;
+    }
+  }
+    
+  return @factors;
+}
+
+sub divisors ($number)
+{
+  my @divisors;
+  
+  for my $candidate (2 .. $number/2)
+  {
+    push(@divisors, $candidate) if $number % $candidate == 0;
+  }
+  
+  return @divisors;
+}
+
+sub is_powerful ($number)
+{
+  return 1 if $number == 1;
+
+  my @factors = factors($number);
+
+  my %values;
+
+  for my $val (@factors)
+  {
+    $values{$val}++;
+  }
+  
+  for my $count (values %values)
+  {
+    return 0 if $count == 1;
+  }
+
+  return 1;
+}
+
+sub is_perfect ($number)
+{
+  return 1 if $number <= 1;
+
+  my @divisors = divisors($number);
+
+  return 0 unless @divisors;
+
+  for my $divisor (@divisors)
+  {
+    my $current = $divisor;
+
+    $current *= $divisor while $current < $number;
+
+    return 1 if $current == $number;
+  }
+
+  return 0;
+}
+
+sub is_achilles ($number)
+{
+  return 0 unless is_powerful($number);
+  return 0 if     is_perfect($number);
+  return 1;
+}
diff --git a/challenge-169/arne-sommer/perl/brilliant-numbers-perl b/challenge-169/arne-sommer/perl/brilliant-numbers-perl
new file mode 100755
index 0000000000..5a6a78d790
--- /dev/null
+++ b/challenge-169/arne-sommer/perl/brilliant-numbers-perl
@@ -0,0 +1,53 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+no warnings 'experimental::signatures';
+
+use Math::Prime::Util 'is_prime';
+
+my $count = shift(@ARGV) || 20;
+
+die "Please specify a positive integer" unless $count =~ /^[1-9]\d*$/;
+
+my @bn = ();
+
+my $candidate = 0;
+
+while (@bn != $count)
+{
+  $candidate++;
+
+  push(@bn, $candidate) if is_brilliant($candidate);
+}
+
+say join(", ", @bn);
+
+sub factors ($number)
+{
+  return (1)       if $number == 1;
+  return ($number) if is_prime($number);
+
+  my @factors;
+
+  for my $candidate (grep { is_prime($_) } 2 .. $number / 2)
+  {
+    while ($number % $candidate == 0)
+    {
+      push(@factors, $candidate);
+      $number /= $candidate;
+    }
+  }
+    
+  return @factors;
+}
+
+sub is_brilliant ($number)
+{
+  my @factors = factors($number);
+  return 0 unless @factors == 2;
+  return 0 unless length($factors[0]) == length($factors[1]);
+  return 1;
+}
diff --git a/challenge-169/arne-sommer/perl/ch-1.pl b/challenge-169/arne-sommer/perl/ch-1.pl
new file mode 100755
index 0000000000..5a6a78d790
--- /dev/null
+++ b/challenge-169/arne-sommer/perl/ch-1.pl
@@ -0,0 +1,53 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+no warnings 'experimental::signatures';
+
+use Math::Prime::Util 'is_prime';
+
+my $count = shift(@ARGV) || 20;
+
+die "Please specify a positive integer" unless $count =~ /^[1-9]\d*$/;
+
+my @bn = ();
+
+my $candidate = 0;
+
+while (@bn != $count)
+{
+  $candidate++;
+
+  push(@bn, $candidate) if is_brilliant($candidate);
+}
+
+say join(", ", @bn);
+
+sub factors ($number)
+{
+  return (1)       if $number == 1;
+  return ($number) if is_prime($number);
+
+  my @factors;
+
+  for my $candidate (grep { is_prime($_) } 2 .. $number / 2)
+  {
+    while ($number % $candidate == 0)
+    {
+      push(@factors, $candidate);
+      $number /= $candidate;
+    }
+  }
+    
+  return @factors;
+}
+
+sub is_brilliant ($number)
+{
+  my @factors = factors($number);
+  return 0 unless @factors == 2;
+  return 0 unless length($factors[0]) == length($factors[1]);
+  return 1;
+}
diff --git a/challenge-169/arne-sommer/perl/ch-2.pl b/challenge-169/arne-sommer/perl/ch-2.pl
new file mode 100755
index 0000000000..1a4c199378
--- /dev/null
+++ b/challenge-169/arne-sommer/perl/ch-2.pl
@@ -0,0 +1,105 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+no warnings 'experimental::signatures';
+
+use Math::Prime::Util 'is_prime';
+
+my $count = shift(@ARGV) || 20;
+
+die "Please specify a positive integer" unless $count =~ /^[1-9]\d*$/;
+
+my @achilles = ();
+
+my $candidate = 0;
+
+while (@achilles != $count)
+{
+  $candidate++;
+
+  push(@achilles, $candidate) if is_achilles($candidate);
+}
+
+say join(", ", @achilles);
+
+sub factors ($number)
+{
+  return (1)       if $number == 1;
+  return ($number) if is_prime($number);
+
+  my @factors;
+
+  for my $candidate (grep { is_prime($_) } 2 .. $number / 2)
+  {
+    while ($number % $candidate == 0)
+    {
+      push(@factors, $candidate);
+      $number /= $candidate;
+    }
+  }
+    
+  return @factors;
+}
+
+sub divisors ($number)
+{
+  my @divisors;
+  
+  for my $candidate (2 .. $number/2)
+  {
+    push(@divisors, $candidate) if $number % $candidate == 0;
+  }
+  
+  return @divisors;
+}
+
+sub is_powerful ($number)
+{
+  return 1 if $number == 1;
+
+  my @factors = factors($number);
+
+  my %values;
+
+  for my $val (@factors)
+  {
+    $values{$val}++;
+  }
+  
+  for my $count (values %values)
+  {
+    return 0 if $count == 1;
+  }
+
+  return 1;
+}
+
+sub is_perfect ($number)
+{
+  return 1 if $number <= 1;
+
+  my @divisors = divisors($number);
+
+  return 0 unless @divisors;
+
+  for my $divisor (@divisors)
+  {
+    my $current = $divisor;
+
+    $current *= $divisor while $current < $number;
+
+    return 1 if $current == $number;
+  }
+
+  return 0;
+}
+
+sub is_achilles ($number)
+{
+  return 0 unless is_powerful($number);
+  return 0 if     is_perfect($number);
+  return 1;
+}
diff --git a/challenge-169/arne-sommer/raku/achilles-numbers b/challenge-169/arne-sommer/raku/achilles-numbers
new file mode 100755
index 0000000000..75ce3d9c1a
--- /dev/null
+++ b/challenge-169/arne-sommer/raku/achilles-numbers
@@ -0,0 +1,92 @@
+#! /usr/bin/env raku
+
+unit sub MAIN (Int :c(:$count) where $count > 0 = 20, :$powerful, :$perfect);
+
+my $bn;
+
+
+if ($powerful && ! $perfect)
+{
+  $bn := (1 .. Inf).grep( *.&is-powerful );
+}
+elsif ($perfect && !$powerful)
+{
+  $bn := (1 .. Inf).grep( *.&is-perfect );
+}
+else
+{
+  $bn := (1 .. Inf).grep( *.&is-achilles );
+}
+
+say $bn[^$count].join(", ");
+
+sub factors ($number is copy)
+{
+  return (1)       if $number == 1;
+  return ($number) if $number.is-prime;
+
+  my @factors;
+
+  for (2 .. $number div 2).grep( *.is-prime) -> $candidate
+  {
+    while $number %% $candidate
+    {
+      @factors.push: $candidate;
+      $number /= $candidate;
+    }
+  }
+
+  return @factors;
+}
+
+sub divisors ($number,