Vampire numbers

True vampires, such as in the two previous examples, have an even number of digits, and each one of the multiplicands has half the number of digits of the vampire. Of most interest to me are true vampires that are not created by simply adding O s to the ends of numbers, as in 270,000 x 810,000 = 218,700,000,000. [Pg.227]

On April 29, 1994,1 challenged computer scientists and mathematicians around the world to submit the largest vampire number they could find. It turns out that there are certain situations in which arbitrarily large, pseudovampire numbers can be found. Pseudovampires are numbers that have the same properties as vampires, but the two multiplicands have a different number of digits. After reading my chal-... [Pg.227]

Upon hearing of my interest in vampire numbers, Tony Davie from Scotland found other four-digit pseudovampires. He wrote the following Gofer program to perform the search ... [Pg.228]

Dick Adams from Maryland suggests that we refer to the largest vampire number as vampire omega. ... [Pg.228]

Finally, Dean Hickerson notes that if we allow researchers to add zeros to the interior of numbers, large vampires can be created, as in ... [Pg.228]

In general. Dean uses Mathematica to search for vampire numbers. Below is a chunk of a Mathematica program ... [Pg.228]

Most important. Cliff has the distinction as having found the largest true vampire number to date, excluding those that can be formed by adding more and more zeros to the interior of numbers ... [Pg.229]

Notice that this number has a shared vampire factor with the previous and does not contain any zeros. Can you beat these 20-digit monstrosities They required a few hours of computation on a 486 PS/2. [Pg.229]

NB. vampa looks for vampire associates of numbers on left NB. from the list on right... [Pg.230]

As the numbers get larger and larger, how often do you expect to find vampires Do they become more secretive (sparser) or more outgoing (frequent) as one searches for vampires up to a googol ... [Pg.231]

Even though there are more vampires in each log range, vampires are actually becoming less dense in each range. (Is this strange considering that large numbers have more factors than smaller ones )... [Pg.231]

Similarly, Stephen H. Landrum from California suggests that the ratio V /n (where Vj, is the number of vampire numbers up to n) will in general decrease as n gets larger, but the ratio Vylogin) will increase as n gets larger. [Pg.231]

What is the largest true vampire number you can find lurking out there in the world of integers Glenn S. Knickerbocker from New York notes that no vampires or pseudovampires are products of two vampires or pseudovampires with six or fewer digits. [Pg.231]

As additional research in vampire numbers, Tony left (a slightly modified) version of his Gofer program running for a long time on his computer ... [Pg.281]

Steve Frye from North Carolina used the following REXX program on a VM system to search for vampire numbers. [Pg.281]

Another REXX Program to Search for Vampire Numbers... [Pg.286]

PRINT "There were VampireCount " distinct vampire numbers found."... [Pg.294]

Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...