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A vampire number (or true vampire number) is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains all the digits from x and from y, in any order. x and y are called the fangs.
For example: 1260 is a vampire number, with 21 and 60 as fangs, since 21 × 60 = 1260. However, 126000 – 210 × 600 – is not, as both 210 and 600 have trailing zeroes.
Vampire numbers first appeared in a 1994 post by Clifford A. Pickover to the Usenet group sci.math, and the article he later wrote was published in chapter 30 of his book Keys to Infinity. The vampire numbers are (sequence A014575 in OEIS):
| n
| Vampire numbers of length n
|
| 4
| 7
|
| 6
| 148
|
| 8
| 3228
|
| 10
| 108454
|
| 12
| 4390670
|
| 14
| 208423682
|
A vampire number can have multiple distinct pairs of fangs, though most have only one pair.
Variants
Pseudovampire numbers are similar to vampire numbers, except that the fangs of an n-digit pseudovampire number need not be of length n/2 digits. Because of this, then, pseudovampire numbers need not have an even number of digits.
A prime vampire number, as defined by Carlos Rivera in 2002, is a true vampire number whose fangs are its prime factors. The first few prime vampire numbers are:
- 117067, 124483, 146137, 371893, 536539
References
External links
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