In mathematics, a vampire number is a number that can be obtained by multiplying two numbers of equal length (the fangs) whith every digit occurs in both factors.
Definition
The 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.
Origin
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.
Examples
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.
List
- 21 x 60 = 1260
- 15 x 93 = 1395
- 35 x 41 = 1435
- 30 x 51 = 1530
- 21 x 87 = 1827
- 27 x 81 = 2187
- 80 x 86 = 6880
- 102510, 104260, 105210, 105264, 105750, 108135, 110758, 115672, 116725, 117067, 118440, 120600, 123354, 124483, 125248, 125433, 125460, 125500, ... (sequence A014575 in OEIS)
References
- Pickover, Clifford A. (1995). Keys to Infinity. Wiley. ISBN 0-471-19334-8
- Pickover's original post describing vampire numbers
- Andersen, Jens K. Vampire Numbers
- Rivera, Carlos. The Prime-Vampire numbers
- Schneider, Walter. Vampire Numbers