Merge remote-tracking branch 'upstream/master'

20 files changed, 2343 insertions, 1906 deletions

diff --git a/challenge-168/0rir/raku/ch-1.raku b/challenge-168/0rir/raku/ch-1.raku
new file mode 100644
index 0000000000..174f2651a5
--- /dev/null
+++ b/challenge-168/0rir/raku/ch-1.raku
@@ -0,0 +1,40 @@
+#!/usr/bin/env raku
+# :vim ft=raku sw=4 expandtab
+use v6.d;
+
+use lib $?FILE.IO.parent(2).add("lib");
+use Test;
+=begin comment
+
+Task 1: Perrin Prime    Submitted by: Roger Bell_West
+The Perrin sequence is defined to start with [3, 0, 2]; thereafter term N
+is the sum of terms N-2 and N-3.
+
+A Perrin prime is a prime number in the Perrin sequence.
+Calculate the first 13 Perrin Primes.
+
+=end comment
+
+my @exp-perrin = 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39;
+my @exp-per-rime = 2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977;
+
+my Int @Perrin = 3, 0, 2, { $_ = @_[*-3] + @_[*-2] } … ∞;
+
+my @Perrin-prime = lazy gather {
+    my %seen;
+    for 2 … ∞  -> $i {      # skip out of order dupes
+        if @Perrin[$i].is-prime { 
+            take @Perrin[$i] unless %seen{@Perrin[$i]};
+            %seen{@Perrin[$i]} = True;
+        }
+    }
+};
+say 'f(13) = [' ~ @Perrin-prime[0..12].join( ',') ~ ']';
+say '';
+
+plan 2;
+is @Perrin[0..13], @exp-perrin, 'Perrin';
+is @Perrin-prime[0..12] , @exp-per-rime, '@Perrin-prime[0..12] ';
+done-testing;
+
+
diff --git a/challenge-168/0rir/raku/ch-2.raku b/challenge-168/0rir/raku/ch-2.raku
new file mode 100644
index 0000000000..631aed6970
--- /dev/null
+++ b/challenge-168/0rir/raku/ch-2.raku
@@ -0,0 +1,57 @@
+#!/usr/bin/env raku
+# :vim ft=raku sw=4 expandtab
+use v6.d;
+use Test;
+use Prime::Factor; # better than my simple implementation from challenge-159
+
+constant TEST = False;
+
+=begin comment
+Task 2: Home Prime Submitted by: Mohammad S Anwar
+
+Given an integer greater than 1, find the home prime of the given number.
+The home prime HP(n) of that integer, n, is the first prime number obtained
+by repeatedly factoring the increasing concatenation of prime factors
+including repetitions.
+
+Example of procedure.
+n    f    !prime     !prime        !prime       home prime
+10 ~ 2*5 -> 25 ~ 5*5 -> 55 ~ 5*11 -> 511 ~ 7*73 -> 773
+
+=end comment
+
+my constant @prime is export
+        = 2, 3, { first * %% none(@_), (@_[*-1], *+2 … ∞)} … ∞;
+
+sub home-prime( Int $n is copy where $n > 1 --> Int ) {
+    until $n.is-prime {
+        $n = ([~] prime-factors( $n)).Int;
+    }
+    $n;
+}
+
+if TEST {
+
+    my @expected =
+        1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223,
+        13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37,
+        211, 23, 331319, 773, 3251, 13367, 227, 29, 547, 31, 241271, 311,
+        31397, 1129, 71129, 37, 373, 313, 3314192745739, 41, 379, 43,
+        22815088913, 3411949, 223, 47, 6161791591356884791277;
+
+    plan  @expected.elems ;
+
+    is True, True, 'NOOP: Tests are on test number.';
+    my $i = 2;
+    for 2 .. @expected.elems  {
+        my $hp = home-prime $_;
+        is $hp, @expected[$i -1], "hp $hp";
+        ++ $i;
+    }
+    exit;
+}
+
+sub MAIN(Int $n where $n > 1 ) {
+    say "The home prime of $n is ", home-prime( $n);
+}
+
diff --git a/challenge-168/jo-37/perl/ch-1.pl b/challenge-168/jo-37/perl/ch-1.pl
new file mode 100755
index 0000000000..8351305463
--- /dev/null
+++ b/challenge-168/jo-37/perl/ch-1.pl
@@ -0,0 +1,155 @@
+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0 '!array';
+use bigint;
+use List::Gen qw(:iterate :zip :source);
+use List::Util qw(product);
+use Math::Prime::Util qw(is_prime gcd);
+use experimental qw(signatures postderef);
+
+our ($tests, $examples, $iv, $f);
+$iv ||= '3, 0, 2';
+$f ||= '1, 1';
+
+run_tests() if $tests || $examples;	# does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [-tests] [-f=F1,...,Fl] [-iv=S1,...Sk] [N]
+
+-examples
+    run the examples from the challenge
+ 
+-tests
+    run some tests
+
+-f=F1,...,Fl
+    Coefficients for the linear recurrence relation.
+
+-iv=S1,...,Sk
+    Starting values for the generated sequence.
+
+N
+    Print the first N prime numbers from the generated sequence.
+
+    The sequence starts with the values S1,...,Sk and has the
+    linear recurrence relation:
+    S(n) = F(1) * S(n - k) + ... + F(k) * S(n - 1) for n > k.
+    Selecting unique primes from this sequence.
+
+Some known prime sequences:
+IV=0,1   F=1,1: Fibonacci
+IV=2,1   F=1,1: Lucas
+IV=1,1,1 F=1,1: Padovan
+IV=3,0,2 F=1,1: Perrin (default)
+IV=0,1   F=1,2: Pell
+IV=0,1   F=2,1: Jacobsthal
+
+CAUTION: Improper choice of IV and F will cause an endless loop!
+
+EOS
+
+
+### Input and Output
+
+main: {
+    # Explicit conversion to Math::BigInt is required for a set of
+    # variables so that all newly generated values inherit therefrom.
+    # Linear factors:
+    my $f = [map Math::BigInt->new($_), split /, */, $f];
+    # Initial values:
+    my $iv = [split /, */, $iv];
+
+    # "say(n)" prints the first n generated elements.
+    lin_recur_primes($iv, $f)->say(shift);
+}
+
+
+### Implementation
+
+# The solution to task 2 from challenge 154 with different starting
+# values could be reused to solve this task.  But this would by boring
+# and thus the task will be generalized here.
+#
+# The excellent Math::Prime::Util ennobles List::Gen by referencing it in
+# the "SEE ALSO" section.  Indeed, it looks very cool but comes with a
+# serious flaw: There has not been any development for over 10 years and
+# one of the tests is broken.  Needed "--force" to install. IMHO the
+# test result is ok, but the expected outcome is not.
+# "Failed test 'map & \(1 .. 3), 1 .. 2'"
+#
+# Building a generator for a sequence having the initial values
+# S(1),...,S(k) and a recurrence relation defined by a linear
+# combination of preceding elements:
+# S(n) = F(1) * S(n - k) + ... + F(k) * S(n - 1) for n > k.
+# and taking unique primes thereof.
+#
+sub lin_recur_primes ($s, $f) {
+
+    # Lazily extend the initial sequence using the recurrence relation.
+    ($s + iterate {($s = [$s->@[1 .. $#$s],
+                    tuples($f, $s)->map('product @$_')->sum])->[-1]
+        })->uniq->filter(sub {is_prime $_});
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    SKIP: {
+        skip "examples" unless $examples;
+
+        # "take" returns the given number of elements.
+        is lin_recur_primes([3, 0, 2], [1, 1])->take(13),
+        [3, 2, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193,
+            792606555396977], 'task 1';
+    }
+
+    SKIP: {
+        skip "tests" unless $tests;
+
+        # "get" accesses elements by a zero-based index.  Thus "get(15)"
+        # is *three* behind the last from "take(13)".
+        is lin_recur_primes([3, 0, 2], [1, 1])->get(15),
+        '22584751787583336797527561822649328254745329',
+        'Perrin prime from http://oeis.org/A074788';
+
+        is lin_recur_primes([0, 1], [1, 1])->take(11),
+        [2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437,
+            2971215073],
+            'Fibonacci primes from Wiki';
+
+        is lin_recur_primes([1, 1, 1], [1, 1])->take(12),
+        [2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057,
+            1363005552434666078217421284621279933627102780881053358473,
+            1558877695141608507751098941899265975115403618621811951868598809164180630185566719],
+            'Padovan primes from Wiki';
+        
+        is lin_recur_primes([2, 1], [1, 1])->take(15),
+        [2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349,
+            54018521, 370248451, 6643838879],
+            'Lucas primes from Wiki';
+
+        is lin_recur_primes([3, 1], [1, 1])->take(20),
+        [3, 5, 23, 37, 97, 157, 1741, 11933, 50549, 214129, 560597,
+            16276621, 180510493, 398386576261, 1042989597313,
+            41305516996050613, 174972977841043309, 13300248193487978669,
+            238663270054423392193, 624828552868675407173],
+            'A091157';
+
+        is lin_recur_primes([0, 1], [1, 2])->take(8),
+        [2, 5, 29, 5741, 33461, 44560482149, 1746860020068409,
+            68480406462161287469],
+            'Pell primes from Wiki';
+
+        is lin_recur_primes([0, 1], [2, 1])->take(15),
+        [3, 5, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883,
+            2932031007403, 768614336404564651, 201487636602438195784363,
+            845100400152152934331135470251,
+            56713727820156410577229101238628035243],
+            'Jacobsthal primes from Wiki';
+	}
+
+    done_testing;
+    exit;
+}
diff --git a/challenge-168/perlboy1967/perl/ch-1.pl b/challenge-168/perlboy1967/perl/ch-1.pl
new file mode 100755
index 0000000000..50073d073d
--- /dev/null
+++ b/challenge-168/perlboy1967/perl/ch-1.pl
@@ -0,0 +1,51 @@
+#!/bin/perl
+
+=pod
+
+The Weekly Challenge - 168
+ - https://theweeklychallenge.org/blog/perl-weekly-challenge-168/#TASK1
+
+Author: Niels 'PerlBoy' van Dijke
+
+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]
+
+=cut
+
+use v5.16;
+use warnings;
+
+use Math::Prime::XS qw(is_prime);
+
+# Prototype(s)
+sub perrin ($);
+
+my %p;
+my ($n,$p) = (0,1);
+while ($n < 13) {
+  my $pN = perrin($p++);
+  if (is_prime($pN) && !exists $p{$pN}) {
+    say $pN; $p{$pN}++; $n++;
+  }
+}
+  
+sub perrin ($) {
+  my ($n) = @_;
+
+  state $p = [3, 0, 2];
+
+  return $p->[$n] if defined $p->[$n];
+
+  $p->[@$p] = $p->[@$p-2] + $p->[@$p-3] while (!defined $p->[$n]);
+
+  return $p->[$n];
+}
diff --git a/challenge-168/perlboy1967/perl/ch-2.pl b/challenge-168/perlboy1967/perl/ch-2.pl
new file mode 100755
index 0000000000..6f710f9110
--- /dev/null
+++ b/challenge-168/perlboy1967/perl/ch-2.pl
@@ -0,0 +1,47 @@
+#!/bin/perl
+
+=pod
+
+The Weekly Challenge - 168
+ - https://theweeklychallenge.org/blog/perl-weekly-challenge-168/#TASK2
+
+Author: Niels 'PerlBoy' van Dijke
+
+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.
+
+=cut
+
+use v5.16;
+use warnings;
+
+use Math::Prime::XS qw(is_prime);
+use Math::Factor::XS qw(prime_factors);
+use Try::Tiny;
+
+# prototype(s)
+sub homePrime ($);
+
+for my $n (2 .. 1000) {
+  my  $h = homePrime($n);
+  printf "%d\t=> %s\n", $n, (!defined $h ? 'Too big to handle' : $h);
+}
+
+sub homePrime ($) {
+  my ($n) = @_;
+
+  try { $n  = join '', prime_factors($n) while (!is_prime($n)) }
+  catch { return };
+
+  return $n;
+}
diff --git a/challenge-168/steve-g-lynn/raku/ch-2.p6 b/challenge-168/steve-g-lynn/raku/ch-2.p6
index b4183fd6d3..bfe46ec923 100755
--- a/challenge-168/steve-g-lynn/raku/ch-2.p6
+++ b/challenge-168/steve-g-lynn/raku/ch-2.p6
@@ -1,44 +1,66 @@
 #!/usr/bin/raku
 
+#time (bash command): 
+#real	0m0.490s
+#user	0m0.729s
+#sys	0m0.056s
+
+
+# acknowledgement:
+
+# I improved the previous grossly inefficient version 
+# (> 1 min script run time) after looking 
+# at the raku and python submissions from Roger Bell-West
+
+
+say homeprime(10);
+#773
 say homeprime(16);
-# 31636373
-#-- works but slow
+#31636373
 
 #-- sub for home prime
 
-sub homeprime(Int $n){
+sub homeprime(Int $n) returns Int { 
+	$n.Int.is-prime && return $n;
 	my $ncopy=$n;
 	while (1) {
-		$ncopy=factor($ncopy).Int;
-		($ncopy.is-prime) && last;
+		my $last=$ncopy;
+		$ncopy=factor($ncopy);
+		($ncopy==$last) && last;
 	}
 	return $ncopy;
 }
 
 #--sub for factorizing
 
-multi sub factor (1) {1}
+multi sub factor (1) returns Int {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;
+multi sub factor (Int $n where $n > 1) returns Int {
+#-- returns the concatenated prime factors as an int
+	$n.Int.is-prime && (return $n.Int );
+	my $sqrt_n = sqrt($n).Int+1;
+	my @primes=find_primes($sqrt_n);
+	my @factors=();
 
-	($n.is-prime) && (return $n);	
+	my $retstring="";
+	my $ncopy=$n;	
 	
 	for @primes -> $prime {
 		while ( ($ncopy % $prime)==0) {
 			$ncopy /= $prime;
-			$retstring ~= $prime;
+			push @factors, $prime;
 		}
 	}
-	return $retstring;
+	($ncopy > 1) && push @factors, $ncopy;
+	#-- any factor bigger than sqrt(n) is a prime factor
+	$retstring = @factors.list.join;
+
+	return $retstring.Int;
 }
 
-multi sub find_primes(Int $n where $n <= 13) {
-	my @primes=(2,3,5,7,11,13);
+multi sub find_primes(Int $n where $n <= 100) {
+	my @primes=
+	(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97); 
 	my @retval=();
 	for @primes -> $prime {
 		($prime < $n) && (push @retval, $prime);
@@ -46,39 +68,59 @@ multi sub find_primes(Int $n where $n <= 13) {
 	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);
+multi sub find_primes (Int $n where $n > 100) {
+	my @primes=[7,11,13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]; #-- candidate primes
+	my %primes{Int}=(); #-- we will return keys of this
+	my $sqrt_n = sqrt($n); #-- ceiling for iterating thru' sieve
+	
+	#-- initialize primes hash
+	#-- store candidates of the form 6k-1 to 6k+1
+	#-- eliminate multiples of known primes
+	loop (my $i=102; $i <= $n+1; $i += 6) {
+		my @temp=($i-1, $i+1);
+		TEMP: for @temp -> $temp {
+			($temp % 3) || next;
+			($temp % 5) || next;
+			for @primes -> $prime {
+				($prime > $sqrt_n) && last;
+				($temp % $prime) || next TEMP;
+			}
+			($temp <= $n) && (%primes{$temp}=True);
+		}
+	}
+		
+	#-- for prime candidates k greater than @primes[*-1]
+	#-- use odd numbers not divisible by 3 (last value + 4 and +6 if
+	#   we start counting from 97)
+	#-- loop through factors kk+jk < n and delete
+	#-- any %hash entries with key matching these factors.
+
+	my $last_prime = @primes[*-1];
+	if ($last_prime < $sqrt_n) { 
+		@primes=[$last_prime+4, $last_prime+2];
+		while (1) {
+			my $prime = shift @primes;
+			(@primes.elems==0) && 
+				(@primes.append($prime+4, $prime+2));
+			#-- avoid multiples of 3
+			
+			last if $prime > $sqrt_n;
+		
+			#-- only loop if the candidate is in the primes hash
+			if  ( %primes{$prime} ) {
+				loop (my $i=$prime*$prime; 
+					$i <= $n;
+					$i += $prime) {
+						%primes{$i}:delete;
+				}
+			}
+		}
+	}
+	my @retval=(2,3,5,7,11,13,17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97);
+	return (@retval.append(%primes.keys.sort));
+
+	return 1;
 }
 
 
+
diff --git a/stats/pwc-current.json b/stats/pwc-current.json
index bd43401c7c..14e65eb85c 100644
--- a/stats/pwc-current.json
+++ b/stats/pwc-current.json
@@ -1,29 +1,155 @@
 {
+   "series" : [
+      {
+         "name" : "The Weekly Challenge - 168",
+         "colorByPoint" : 1,
+         "data" : [
+            {
+               "y" : 2,
+               "drilldown" : "E. Choroba",
+               "name" : "E. Choroba"
+            },
+            {
+               "drilldown" : "Humberto Massa",
+               "y" : 2,
+               "name" : "Humberto Massa"
+            },
+            {
+               "name" : "James Smith",
+               "drilldown" : "James Smith",
+               "y" : 3
+            },
+            {
+               "name" : "Jorg Sommrey",
+               "y" : 1,
+               "drilldown" : "Jorg Sommrey"
+            },
+            {
+               "name" : "Julien Fiegehenn",
+               "y" : 2,
+               "drilldown" : "Julien Fiegehenn"
+            },
+            {
+               "drilldown" : "Lubos Kolouch",
+               "y" : 1,
+               "name" : "Lubos Kolouch"
+            },
+            {
+               "drilldown" : "Luca Ferrari",
+               "y" : 8,
+               "name" : "Luca Ferrari"
+            },
+            {
+               "drilldown" : "Mark Anderson",
+               "y" : 2,
+               "name" : "Mark Anderson"
+            },
+            {
+               "drilldown" : "Marton Polgar",
+               "y" : 2,
+               "name" : "Marton Polgar"
+            },
+            {
+               "name" : "Niels van Dijke",
+               "y" : 2,
+               "drilldown" : "Niels van Dijke"
+            },
+            {
+               "name" : "Peter Campbell Smith",
+               "drilldown" : "Peter Campbell Smith",
+               "y" : 3
+            },
+            {
+               "name" : "Robert DiCicco",
+               "drilldown" : "Robert DiCicco",
+               "y" : 4
+            },
+            {
+               "name" : "Robert Ransbottom",
+               "y" : 2,
+               "drilldown" : "Robert Ransbottom"
+            },
+            {
+               "y" : 5,
+               "drilldown" : "Roger Bell_West",
+               "name" : "Roger Bell_West"
+            },
+            {
+               "y" : 6,
+               "drilldown" : "Ryan Thompson",
+               "name" : "Ryan Thompson"
+            },
+            {
+               "y" : 4,
+               "drilldown" : "Stephen G Lynn",
+               "name" : "Stephen G Lynn"
+            },
+            {
+               "name" : "W. Luis Mochan",
+               "y" : 3,
+               "drilldown" : "W. Luis Mochan"
+            }
+         ]
+      }
+   ],
+   "yAxis" : {
+      "title" : {
+         "text" : "Total Solutions"
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-            "name" : "James Smith",
             "data" : [
                [
                   "Perl",
@@ -33,30 +159,40 @@
                   "Blog",
                   1
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+            ],
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                   "Perl",
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@@ -67,21 +203,22 @@
                   "Blog",
                   6
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                   "Raku",
@@ -90,6 +227,17 @@
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@@ -100,12 +248,9 @@
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@@ -115,10 +260,21 @@
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                   2
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+                  "Raku",
+                  2
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@@ -133,11 +289,10 @@
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-            "id" : "Ryan Thompson",
             "data" : [
                [
                   "Perl",
@@ -151,11 +306,11 @@
                   "Blog",
                   2
                ]
-            ]
+            ],
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+            "id" : "Ryan Thompson"
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-            "id" : "Stephen G Lynn",
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                [
                   "Perl",
@@ -165,11 +320,13 @@
                   "Raku",
                   2
                ]
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+            ],
+            "name" : "Stephen G Lynn",
+            "id" : "Stephen G Lynn"
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-            "name" : "W. Luis Mochan",
             "id" : "W. Luis Mochan",
+            "name" : "W. Luis Mochan",
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                   "Perl",
@@ -182,117 +339,5 @@
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