#!/usr/bin/perl
use v5.10;
use strict;
use warnings;

use Data::Dumper;

my $series = [3, 9, 7, 3, 13, 5, 45];

my $permut = 1;
$permut *= $_ for (@$series);

my $chunks = 4;#int($permut/100_000_000);
$chunks = $chunks < 1 ? 1 : $chunks;

my $chunk_size = int($permut / $chunks);
my $chunk_start = 1;
my $chunk_end   = $chunk_size;

say join ' ', @$series;
say "Permutations: $permut\tChunk size:\t$chunk_size\tChunks:\t$chunks";

my @chunk_ranges;
while ($chunk_end <= $permut) {
        push @chunk_ranges, [ [$chunk_start, cpns($series, $chunk_start)], [$chunk_end, cpns($series, $chunk_end)] ];
        
        $chunk_start    +=      $chunk_size;    
        $chunk_end              +=      $chunk_size;
}

#last chunk_end contains the rest $permut/$chunk_size gives,
#consequential it equals the amount of permutations-1
$chunk_ranges[-1]->[-1] = [$permut, cpns($series, $permut-1)];

print Dumper \@chunk_ranges;

sub cpns  { convert_positional_notation_systems(@_) };
sub convert_positional_notation_systems {
        my $bases               = shift;
        my $quotient    = shift;        
        my $rest;
        my @result;

        for my $base (reverse @$bases) {
                $rest           = $quotient % $base;
                $quotient       = int($quotient / $base);
                push @result, $rest;
                
                last if $quotient == 0;
        }

        @result = reverse @result;
        return join ' ', @result;
        return \@result;
}

3 9 7 3 13 5 45
Permutations: 1658475   Chunk size:     414618  Chunks: 4
$VAR1 = [
          [
            [
              1,
              '1'
            ],
            [
              414618,
              '6 5 0 9 3 33'
            ]
          ],
          [
            [
              414619,
              '6 5 0 9 3 34'
            ],
            [
              829236,
              '1 4 3 1 6 2 21'
            ]
          ],
          [
            [
              829237,
              '1 4 3 1 6 2 22'
            ],
            [
              1243854,
              '2 2 1 2 3 1 9'
            ]
          ],
          [
            [
              1243855,
              '2 2 1 2 3 1 10'
            ],
            [
              1658475,
              '2 8 6 2 12 4 44'
            ]
          ]
        ];