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 = 21 ⋅ 60, 1395 = 15 ⋅ 93, 1435 = 35 ⋅ 41, 1530 = 30 ⋅ 51 and 1827 = 21 ⋅ 87.

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 = 246 ⋅ 510 = 204 ⋅ 615 and
13078260 = 1620 ⋅ 8073 = 1863 ⋅ 7020 = 2070 ⋅ 6318.

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