Vampire number
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
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.
Prime vampire numbers, as defined by Carlos Rivera in 2002, are true vampire numbers where its fangs are its prime factors.
References
Pickover, Clifford A (1995). Keys to Infinity. Wiley. ISBN 0-47-119334-8
