A vampire number is a positive integer 
with an even number 
of decimal
digits, where 
and 
are positive integers with exactly 
decimal digits each. The
combined multiset of their digits
must equal the multiset of the digits
of 
, and 
and 
may not both end in zero. If 
is a vampire number, then 
and 
are called its "fangs." Exchanging the two fangs
does not give a distinct pair. Examples of vampire numbers include
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(1)
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(2)
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(3)
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(4)
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(5)
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(6)
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(7)
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(OEIS A014575). The 8-digit vampire numbers are 10025010, 10042510, 10052010, 10052064, 10081260, ... (OEIS A048938)
and the 10-digit vampire numbers are 1000174288, 1000191991, 1000198206, 1000250010,
... (OEIS A048939). The numbers of 
-digit vampires are 0, 7, 148, 3228, ... (OEIS A048935).
Vampire numbers having exactly two distinct pairs of fangs include
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(8)
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(9)
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(10)
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(OEIS A048936).
Vampire numbers having exactly three distinct pairs of fangs include
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(11)
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(OEIS A048937).
The first vampire numbers with four pairs of fangs are
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(12)
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(13)
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(14)
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(15)
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and
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(16)
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(17)
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(18)
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(19)
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and the first vampire number with five pairs of fangs is
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(20)
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(21)
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(22)
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(23)
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(24)
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(J. K. Andersen, pers. comm., May 4, 2003).
General formulas can be constructed for special classes of vampires. For an integer 
, take the fangs
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(25)
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(26)
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giving the vampire
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(27)
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(28)
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(29)
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(30)
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where 
denotes 
with the digits reversed (Roush and Rogers 1997-1998).
Pickover (1995) also defines pseudovampire numbers, in which the multiplicands have different numbers of digits.
