A number with an even number of digits formed by multiplying a pair of -digit numbers (where the digits are taken from the original number in any order) and together. Pairs of trailing zeros are not allowed. If is a vampire number, then and are called its "fangs." Examples of vampire numbers include
(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 two distinct pairs of fangs include
(8)
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(9)
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(10)
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(OEIS A048936).
Vampire numbers having three distinct pairs of fangs include
(11)
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(OEIS A048937).
The first vampire numbers with four pairs of fangs are
(12)
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(13)
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(14)
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(15)
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and
(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
(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, such as the fangs
(25)
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(26)
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giving the vampire
(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.