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#!/usr/bin/env perl
use strict;
use warnings;
use feature qw{ postderef say signatures state };
no warnings qw{ experimental };
use Carp;
my $i = shift @ARGV;
$i //= 2;
croak 'non-positive integer' if $i < 1;
croak 'not an integer' if $i =~ /\D/;
say join "\n\t", "RARE NUMBERS: $i", rare_numbers($i), '';
# a number r is "rare" when:
# - r1 is that number reversed
# - sqrt(r+r1) is an integer
# - sqrt(r-r1) is an integer
sub rare_numbers ( $i ) {
my @output;
# given i == 5,
# low is 10000, the smallest five-digit number
# high is 99999, the highest five-digit number
my $low = join '', map { $_ == 1 ? 1 : 0 } 1 .. $i;
my $high = 9 x $i;
for my $r ( $low .. $high ) {
my $r1 = reverse $r;
next if $r - $r1 < 0; # early block for thing that break sqrt
my $s1 = sqrt( $r + $r1 );
next if $s1 =~ /\D/; # test if integer
my $s2 = sqrt( $r - $r1 );
next if $s2 =~ /\D/; # test if integer
push @output, $r;
}
return @output;
}
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