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Thursday, July 29, 2010

VAMPIRE NUMBER

The vampire numbers were introduced by Clifford A. Pickover in 1994.

A Vampire number z  is a number which can be written as a product of two numbers x and y  containing the same digits the same number of times as the vampire number. Here x and y are called FANGS.

FOR EXAMPLE:

1827 can be written as a product of two numbers 21 and 87.
i.e., 1827 = 21 * 87
Here the digits 1,8, 2,7 are repeated  the same number of times but in different order. 21 and 87 are called fangs.

A true Vampire number isa number which can be written with 2 fangs having the same number of digits not both ending in zero.

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.

All vampire numbers must clearly have an no. of digits.


Some vampire numbers:
 117067 = 167*701
124483 = 281 * 443
536539 = 563 · 953
23287176 = 2673 * 8712.




Vampire number having two distinct pairs of fangs :


125460 = 204 *615 = 246 * 510

Vampire number having three distinct pairs of fangs :

13078260 = 1620*8073 = 1863*7020 = 2070*6318
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