From 2c57b47bd8eae004c8696e750959b33341072a95 Mon Sep 17 00:00:00 2001
From: arnesom <arne@bbop.org>
Date: Sun, 16 Jan 2022 21:24:50 +0100
Subject: Arne Sommer

---
 challenge-147/arne-sommer/blog.txt                 |  1 +
 challenge-147/arne-sommer/perl/ch-1.pl             | 36 +++++++++++++++++++
 challenge-147/arne-sommer/perl/ch-2.pl             | 40 ++++++++++++++++++++++
 .../arne-sommer/perl/pentagon-numbers-loop-perl    | 40 ++++++++++++++++++++++
 .../arne-sommer/perl/truncatable-prime-perl        | 36 +++++++++++++++++++
 challenge-147/arne-sommer/raku/ch-1.raku           | 20 +++++++++++
 challenge-147/arne-sommer/raku/ch-2.raku           | 31 +++++++++++++++++
 challenge-147/arne-sommer/raku/pentagon-numbers    | 35 +++++++++++++++++++
 .../arne-sommer/raku/pentagon-numbers-loop         | 31 +++++++++++++++++
 .../arne-sommer/raku/pentagon-numbers-loop-cached  | 40 ++++++++++++++++++++++
 .../arne-sommer/raku/pentagon-numbers-seq          | 16 +++++++++
 .../arne-sommer/raku/pentagon-numbers-seq-grep     | 13 +++++++
 challenge-147/arne-sommer/raku/truncatable-prime   | 20 +++++++++++
 13 files changed, 359 insertions(+)
 create mode 100644 challenge-147/arne-sommer/blog.txt
 create mode 100755 challenge-147/arne-sommer/perl/ch-1.pl
 create mode 100755 challenge-147/arne-sommer/perl/ch-2.pl
 create mode 100755 challenge-147/arne-sommer/perl/pentagon-numbers-loop-perl
 create mode 100755 challenge-147/arne-sommer/perl/truncatable-prime-perl
 create mode 100755 challenge-147/arne-sommer/raku/ch-1.raku
 create mode 100755 challenge-147/arne-sommer/raku/ch-2.raku
 create mode 100755 challenge-147/arne-sommer/raku/pentagon-numbers
 create mode 100755 challenge-147/arne-sommer/raku/pentagon-numbers-loop
 create mode 100755 challenge-147/arne-sommer/raku/pentagon-numbers-loop-cached
 create mode 100755 challenge-147/arne-sommer/raku/pentagon-numbers-seq
 create mode 100755 challenge-147/arne-sommer/raku/pentagon-numbers-seq-grep
 create mode 100755 challenge-147/arne-sommer/raku/truncatable-prime

diff --git a/challenge-147/arne-sommer/blog.txt b/challenge-147/arne-sommer/blog.txt
new file mode 100644
index 0000000000..91b6c7d761
--- /dev/null
+++ b/challenge-147/arne-sommer/blog.txt
@@ -0,0 +1 @@
+https://raku-musings.com/pentagon-prime.html
diff --git a/challenge-147/arne-sommer/perl/ch-1.pl b/challenge-147/arne-sommer/perl/ch-1.pl
new file mode 100755
index 0000000000..6cdb8e2900
--- /dev/null
+++ b/challenge-147/arne-sommer/perl/ch-1.pl
@@ -0,0 +1,36 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+use Math::Prime::Util 'is_prime';
+
+no warnings qw(experimental::signatures);
+
+my $limit = int($ARGV[0] || 20);
+
+my @seq;
+
+my $candidate = 1;
+
+while (@seq < $limit)
+{
+  $candidate++;
+  
+  push(@seq, $candidate) if is_left_trunc($candidate);
+}
+
+say join(", ", @seq);
+
+sub is_left_trunc ($prime)
+{
+  return 0 if $prime =~ /0/;
+
+  for my $start (0 .. length($prime) -1)
+  {
+    return 0 unless is_prime(substr($prime, $start));
+  }
+
+  return 1;
+}
diff --git a/challenge-147/arne-sommer/perl/ch-2.pl b/challenge-147/arne-sommer/perl/ch-2.pl
new file mode 100755
index 0000000000..2b230a6a2a
--- /dev/null
+++ b/challenge-147/arne-sommer/perl/ch-2.pl
@@ -0,0 +1,40 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+
+no warnings qw(experimental::signatures);
+
+my $a = 1;
+
+while ($a++)
+{
+  my $b = $a;
+
+  while ($b-- > 1)
+  {
+    my $penta_a = pentagonial($a);
+    my $penta_b = pentagonial($b);
+
+    if (is_pentagonial($penta_a + $penta_b) && is_pentagonial($penta_a - $penta_b))
+    {
+      say "$penta_b $penta_a";
+      exit;
+    }
+  }
+}
+
+sub is_pentagonial($candidate)
+{
+  my $check = (1 + sqrt(1 + 24 * $candidate)) / 6;
+  return int($check) == $check;
+}
+
+sub pentagonial($number)
+{
+  return $number * ( 3 * $number -1) / 2;
+}
+
+say "(no match)";
diff --git a/challenge-147/arne-sommer/perl/pentagon-numbers-loop-perl b/challenge-147/arne-sommer/perl/pentagon-numbers-loop-perl
new file mode 100755
index 0000000000..2b230a6a2a
--- /dev/null
+++ b/challenge-147/arne-sommer/perl/pentagon-numbers-loop-perl
@@ -0,0 +1,40 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+
+no warnings qw(experimental::signatures);
+
+my $a = 1;
+
+while ($a++)
+{
+  my $b = $a;
+
+  while ($b-- > 1)
+  {
+    my $penta_a = pentagonial($a);
+    my $penta_b = pentagonial($b);
+
+    if (is_pentagonial($penta_a + $penta_b) && is_pentagonial($penta_a - $penta_b))
+    {
+      say "$penta_b $penta_a";
+      exit;
+    }
+  }
+}
+
+sub is_pentagonial($candidate)
+{
+  my $check = (1 + sqrt(1 + 24 * $candidate)) / 6;
+  return int($check) == $check;
+}
+
+sub pentagonial($number)
+{
+  return $number * ( 3 * $number -1) / 2;
+}
+
+say "(no match)";
diff --git a/challenge-147/arne-sommer/perl/truncatable-prime-perl b/challenge-147/arne-sommer/perl/truncatable-prime-perl
new file mode 100755
index 0000000000..6cdb8e2900
--- /dev/null
+++ b/challenge-147/arne-sommer/perl/truncatable-prime-perl
@@ -0,0 +1,36 @@
+#! /usr/bin/env perl
+
+use strict;
+use warnings;
+use feature 'say';
+use feature 'signatures';
+use Math::Prime::Util 'is_prime';
+
+no warnings qw(experimental::signatures);
+
+my $limit = int($ARGV[0] || 20);
+
+my @seq;
+
+my $candidate = 1;
+
+while (@seq < $limit)
+{
+  $candidate++;
+  
+  push(@seq, $candidate) if is_left_trunc($candidate);
+}
+
+say join(", ", @seq);
+
+sub is_left_trunc ($prime)
+{
+  return 0 if $prime =~ /0/;
+
+  for my $start (0 .. length($prime) -1)
+  {
+    return 0 unless is_prime(substr($prime, $start));
+  }
+
+  return 1;
+}
diff --git a/challenge-147/arne-sommer/raku/ch-1.raku b/challenge-147/arne-sommer/raku/ch-1.raku
new file mode 100755
index 0000000000..9612aeb142
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/ch-1.raku
@@ -0,0 +1,20 @@
+#! /usr/bin/env raku
+
+unit sub MAIN ($limit = 20, :v(:$verbose));
+
+my $seq = (2 .. Inf).grep(*.&is-left-trunc);
+
+say $seq[^$limit].join(", ");
+
+sub is-left-trunc ($prime)
+{
+  return False if $prime.contains: '0';
+
+  for ^$prime.chars -> $start
+  {
+    say ": Checking $prime -> { $prime.substr($start) } - { $prime.substr($start).is-prime ?? "prime" !! "not prime" }" if $verbose;
+    return False unless $prime.substr($start).is-prime;
+  }
+
+  return True;
+}
diff --git a/challenge-147/arne-sommer/raku/ch-2.raku b/challenge-147/arne-sommer/raku/ch-2.raku
new file mode 100755
index 0000000000..cf3b4226e8
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/ch-2.raku
@@ -0,0 +1,31 @@
+#! /usr/bin/env raku
+
+unit sub MAIN;
+
+for 2 .. Inf -> $a
+{
+  for $a -1 ... 1 -> $b
+  {
+    my $penta-a = pentagonial($a);
+    my $penta-b = pentagonial($b);
+
+    if is-pentagonial($penta-a + $penta-b) && is-pentagonial($penta-a - $penta-b)
+    {
+      say "$penta-b $penta-a";
+      exit;
+    }
+  }
+}
+
+sub is-pentagonial ($candidate)
+{
+  my $check = (1 + (1 + 24 * $candidate).sqrt) / 6;
+  return $check.Int == $check;
+}
+
+sub pentagonial ($number)
+{
+  return $number * ( 3 * $number -1) / 2;
+}
+
+say "(no match)";
diff --git a/challenge-147/arne-sommer/raku/pentagon-numbers b/challenge-147/arne-sommer/raku/pentagon-numbers
new file mode 100755
index 0000000000..e27232f4cd
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/pentagon-numbers
@@ -0,0 +1,35 @@
+#! /usr/bin/env raku
+
+unit sub MAIN ($limit = 10, :v(:$verbose));
+
+my $penta-seq = gather
+{
+  state $index = 0;
+
+  loop
+  {
+    $index++;
+    take $index * ( 3 * $index -1) / 2;
+  }
+}
+
+my @a = $penta-seq[^$limit];
+
+my %is-penta = @a.Set;
+
+for @a -> $a
+{
+  for @a -> $b
+  {
+    next if $b <= $a;
+    say ": Considering $a, $b" if $verbose;
+
+    if %is-penta{$a + $b} && %is-penta{$b - $a}
+    {
+      say "$a, $b";
+      exit;
+    }
+  }
+}
+
+say "(no match)";
diff --git a/challenge-147/arne-sommer/raku/pentagon-numbers-loop b/challenge-147/arne-sommer/raku/pentagon-numbers-loop
new file mode 100755
index 0000000000..cf3b4226e8
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/pentagon-numbers-loop
@@ -0,0 +1,31 @@
+#! /usr/bin/env raku
+
+unit sub MAIN;
+
+for 2 .. Inf -> $a
+{
+  for $a -1 ... 1 -> $b
+  {
+    my $penta-a = pentagonial($a);
+    my $penta-b = pentagonial($b);
+
+    if is-pentagonial($penta-a + $penta-b) && is-pentagonial($penta-a - $penta-b)
+    {
+      say "$penta-b $penta-a";
+      exit;
+    }
+  }
+}
+
+sub is-pentagonial ($candidate)
+{
+  my $check = (1 + (1 + 24 * $candidate).sqrt) / 6;
+  return $check.Int == $check;
+}
+
+sub pentagonial ($number)
+{
+  return $number * ( 3 * $number -1) / 2;
+}
+
+say "(no match)";
diff --git a/challenge-147/arne-sommer/raku/pentagon-numbers-loop-cached b/challenge-147/arne-sommer/raku/pentagon-numbers-loop-cached
new file mode 100755
index 0000000000..b5212b9862
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/pentagon-numbers-loop-cached
@@ -0,0 +1,40 @@
+#! /usr/bin/env raku
+
+unit sub MAIN;
+
+for 2 .. Inf -> $a
+{
+  for $a -1 ... 1 -> $b
+  {
+    my $penta-a = pentagonial($a);
+    my $penta-b = pentagonial($b);
+
+    if is-pentagonial($penta-a + $penta-b) && is-pentagonial($penta-a - $penta-b)
+    {
+      say "$penta-b $penta-a";
+      exit;
+    }
+  }
+}
+
+sub is-pentagonial ($candidate)
+{
+  state @cache;
+  return @cache[$candidate] if @cache[$candidate];
+
+  my $value = (1 + (1 + 24 * $candidate).sqrt) / 6;
+
+  @cache[$candidate] = ( $value.Int == $value );
+
+  return @cache[$candidate];
+}
+
+sub pentagonial ($number)
+{
+  state @cache;
+  return @cache[$number] if @cache[$number];
+
+  return @cache[$number] = $number * ( 3 * $number -1) / 2;
+}
+
+say "(no match)";
diff --git a/challenge-147/arne-sommer/raku/pentagon-numbers-seq b/challenge-147/arne-sommer/raku/pentagon-numbers-seq
new file mode 100755
index 0000000000..a6074f1a5b
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/pentagon-numbers-seq
@@ -0,0 +1,16 @@
+#! /usr/bin/env raku
+
+unit sub MAIN ($limit = 10);
+
+my $penta-seq = gather
+{
+  state $index = 0;
+
+  loop
+  {
+    $index++;
+    take $index * ( 3 * $index -1) / 2;
+  }
+}
+
+say $penta-seq[^$limit].join(", ");
diff --git a/challenge-147/arne-sommer/raku/pentagon-numbers-seq-grep b/challenge-147/arne-sommer/raku/pentagon-numbers-seq-grep
new file mode 100755
index 0000000000..e553813c16
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/pentagon-numbers-seq-grep
@@ -0,0 +1,13 @@
+#! /usr/bin/env raku
+
+unit sub MAIN ($limit = 10);
+
+my $penta-seq = (1..Inf).grep(*.&is-pentagonial);
+
+say $penta-seq[^$limit].join(", ");
+
+sub is-pentagonial ($candidate)
+{
+  my $is = (1 + (1 + 24 * $candidate).sqrt) / 6;
+  return $is.Int == $is;
+}
diff --git a/challenge-147/arne-sommer/raku/truncatable-prime b/challenge-147/arne-sommer/raku/truncatable-prime
new file mode 100755
index 0000000000..9612aeb142
--- /dev/null
+++ b/challenge-147/arne-sommer/raku/truncatable-prime
@@ -0,0 +1,20 @@
+#! /usr/bin/env raku
+
+unit sub MAIN ($limit = 20, :v(:$verbose));
+
+my $seq = (2 .. Inf).grep(*.&is-left-trunc);
+
+say $seq[^$limit].join(", ");
+
+sub is-left-trunc ($prime)
+{
+  return False if $prime.contains: '0';
+
+  for ^$prime.chars -> $start
+  {
+    say ": Checking $prime -> { $prime.substr($start) } - { $prime.substr($start).is-prime ?? "prime" !! "not prime" }" if $verbose;
+    return False unless $prime.substr($start).is-prime;
+  }
+
+  return True;
+}
-- 
cgit