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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

In reply to Re: Vampire Numbers by Abigail-II
in thread Vampire Numbers by YuckFoo

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