In mathematics, 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 precisely all the digits from x and from y, in any order, counting multiplicity. 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 (which can be expressed as 210 × 600) is not, as both 210 and 600 have trailing zeroes. Similarly, 1023 (which can be expressed as 31 × 33) is not, because although 1023 contains all the digits of 31 and 33, the list of digits of the factors does not coincide with the list of digits of the original number.
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:
1260, 1395, 1435, 1530, 1827, 2187, 6880, 102510, 104260, 105210, 105264, 105750, 108135, 110758, 115672, 116725, 117067, 118440, 120600, 123354, 124483, 125248, 125433, 125460, 125500, ... (sequence A014575 in OEIS)
There are many known sequences of infinitely many vampire numbers following a pattern, such as:
- 1530 = 30×51, 150300 = 300×501, 15003000 = 3000×5001, ...
Read more about Vampire Number: Multiple Fang Pairs, Variants
Famous quotes containing the words vampire and/or number:
“I am the wound and the knife!
I am the slap and the cheek!
I am the limbs and the rack,
And the victim and the executioner!
I am the vampire of my own heart.”
—Charles Baudelaire (1821–1867)
“In a number of other cultures, fathers are not relegated to babysitter status, nor is their ability to be primary nurturers so readily dismissed.... We have evidence that in our own society men can rear and nurture their children competently and that men’s methods, although different from those of women, are imaginative and constructive.”
—Kyle D. Pruett (20th century)