in reply to Vampire Numbers
Here's a piece of code that finds all Vampire numbers with
factors smaller than the argument given:
#!/usr/bin/perl
use strict;
use warnings 'all';
my @vampire;
foreach my $s (1 .. shift) {
LOOP:
foreach my $t (1 .. $s) {
my $prod = $s * $t;
my $cat = "$s$t";
foreach my $d (0 .. 9) {
next LOOP unless eval "\$prod =~ y/$d/$d/ ==
\$cat =~ y/$d/$d/";
}
push @vampire => [$prod, $s, $t];
}
}
@vampire = sort {$a > [0] <=> $b > [0]} @vampire;
foreach my $vamp (@vampire) {
printf "%4d * %4d = %8d\n" => @$vamp [1, 2, 0];
}
Note that if there is one vampire number (and there is),
then we have an infinite number of vampire numbers.
Proof: Suppose V = n * m is a vampire number. Then
10 * V = (10 * n) * m is a vampire number as well. qed.
Abigail
Here are the vampire numbers with factors smaller than 100:
21 * 6 = 126
51 * 3 = 153
86 * 8 = 688
60 * 21 = 1260
93 * 15 = 1395
41 * 35 = 1435
51 * 30 = 1530
87 * 21 = 1827
81 * 27 = 2187
86 * 80 = 6880
Re: Re: Formulas for certain 'fangs' by Anonymous Monk on Jun 11, 2002 at 17:26 UTC 
a couple of general formulas such as the the fangs
x = 25.10^k+1
y = 100(10^(k+1)+52)/25
give the vampire
v = xy = (10^(k+1)+52)10^(k+2)+100(10^k+1+52)/25
= x'.10^(k+2)+t
= 8(26+5.10^k)(1+25.10^k)
where x' denotes x with digits reversed  [reply] 

153 is also a plus perfect number or 'armstrong' number
153=1^3+5^3+3^3=1+125+27
 [reply] 
