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vampire numbers
A number with digits is called vampire there exists two numbers and of digits each such that and that and together have the same digits of .

Moreover, to exclude numbers which can be trivially obtained from smaller ones, and cannot end both in '0'.

The first vampire numbers are 1260 = 2160, 1395 = 1593, 1435 = 3541, 1530 = 3051 and 1827 = 2187.

It can be shown easily that when divided by 9 a vampire number has a remainder equal to 0 or 4.

Since is a vampire number, the numbers and are called fangs.

There are many vampire numbers which have more than one pair of fangs, for example 125460 = 246510 = 204615 and
13078260 = 16208073 = 18637020 = 20706318.

J. K. Andersen has found, among many other results, a 70-digit vampire number with 100025 different fang pairs.

The vampire numbers were introduced by Clifford A. Pickover in 1994. Note that other similar definition are possible (and sometimes used). For example, it is possible to relax the constraint on the number of digits of and , or have more terms in the product, like in .

The first vampire numbers are 1260, 1395, 1435, 1530, 1827, 2187, 6880, 102510, 104260, 105210, 105264, 105750, 108135, 110758 more terms

Vampire numbers can also be... (you may click on names or numbers and on + to get more values)