More recreational math here. Again I was reading some
book by Clifford Pickover,
and heard about Vampire Numbers.
A Vampire Number is equal to a product of it's digits
like 1435 = 41 * 35. I think the name comes from a
reference to such a number in an Anne Rice novel.
So I went hunting for more vamps. This program only
looks for products of two factors, it would be interesting
to look for products of more than two factors.
Algorithm is basically to generate a list of orderings
of the digits (1234, 1243, 1342, 1324, ...), not taking
the trouble to eliminate duplicates.
Next each ordering is split at each digit and tested
(1*234, 12*34, 123*4).
Of note is 153. In addition to being a Triangle Number
(1+2+3+...+17), it is also a selfcubereferential number
(1**3 + 5**3 + 3**3), a sum of factorials (1! + 2! + 3! + 4! + 5!),
and a Vampire Number (3 * 51).
VampFoo
Update: The book is 'The Loom of God'. A 40digit Vnum is
listed there: 98765432198765432198 * 98765432198830604534 =
9754610597415368368844499268390128385732, whew!
#!/usr/bin/perl
use strict;
if (@ARGV < 2) {
print STDERR "\nUsage: $0 firstnumber lastnumber\n\n";
}
my ($beg, $end) = @ARGV;
my ($test, $this, $that);
for $test ($beg..$end) {
($this, $that) = factors($test);
if ($this ne '') {
print "$test = $this * $that\n";
}
}
#
sub factors {
my ($target) = @_;
my ($order, $olist);
my ($split, $slist);
$olist = orderings($target);
for $order (@{$olist}) {
#print "$order\n";
$slist = splittings($order);
for $split (@{$slist}) {
#print "$split>[0] $split>[1]\n";
if ($split>[0] * $split>[1] == $target) {
return ($split>[0], $split>[1]);
}
}
}
}
#
sub splittings {
my ($num) = @_;
my (@digits) = split('', $num);
my (@list, @useds);
while (@digits > 1) {
push(@useds, shift(@digits));
push (@list, [join('', @useds), join('', @digits)]);
}
return \@list;
}
#
sub orderings {
my ($num) = @_;
my (@digits) = split('', $num);
my (@list, $sublists, $sub, $this);
if (@digits == 1) { return [$digits[0]]; }
for (1..@digits) {
$this = shift(@digits);
$sublists = orderings(join('', @digits));
for $sub (@{$sublists}) {
push(@list, "$this$sub");
}
push(@digits, $this);
}
return \@list;
}
Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
Read Where should I post X? if you're not absolutely sure you're posting in the right place.
Please read these before you post! —
Posts may use any of the Perl Monks Approved HTML tags:
 a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)

For: 

Use: 
 &   & 
 <   < 
 >   > 
 [   [ 
 ]   ] 
Link using PerlMonks shortcuts! What shortcuts can I use for linking?
See Writeup Formatting Tips and other pages linked from there for more info.

