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A014575 Vampire numbers (definition 2): numbers n with an even number of digits which have a factorization n = i*j where length(i) = length(j) = length(n)/2 and the multiset of the digits of n coincides with the multiset of the digits of i and j. 15
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, 126027, 126846, 129640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The numbers i and j may not both have trailing zeros. Numbers may have more than one such factorization. However, each n is listed only once. [Comment modified by Rick L. Shepherd, Nov 02 2009]

REFERENCES

C. A. Pickover, "Vampire Numbers." Ch. 30 in Keys to Infinity. New York: Wiley, pp. 227-231, 1995.

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..87

Eric Weisstein's World of Mathematics, Vampire Number.

EXAMPLE

1260 = 21*60, 1395 = 15*93, 1435 = 35*41, 1530 = 30*51, etc.

MAPLE

n := 1 :

for dgs from 4 to 10 by 2 do

    for a from 10^(dgs-1) to 10^dgs-1 do

        amset := sort(convert(a, base, 10)) ;

        isv := false ;

        for d in numtheory[divisors](a) do

            m := a/d ;

            if ( m >= d ) then

                dset := convert(d, base, 10) ;

                mset := convert(m, base, 10) ;

                fset := sort([op(dset), op(mset)]) ;

                if fset = amset and nops(dset) = nops(mset) then

                    if (m mod 10 <> 0 ) or (d mod 10 <> 0 ) then

                    printf("%d %d\n", n, a) ;

                    isv := true ;

                    n := n+1 ;

                    end if;

                end if;

            end if;

            if isv then

                break;

            end if;

        end do:

    end do:

end do: # R. J. Mathar, Jan 10 2013

PROG

(PARI) is(n)=my(v=digits(n)); if(#v%2, return(0)); fordiv(n, d, if(#Str(d)==#v/2 && #Str(n/d)==#v/2 && vecsort(v)==vecsort(digits(eval(Str(d, n/d)))) && (d%10 || (n/d)%10), return(1))); 0 \\ Charles R Greathouse IV, Apr 19 2013

CROSSREFS

The following sequences are all closely related: A020342, A014575, A080718, A048936, A144563.

Cf. A048933, A048934, ..., A048939.

Sequence in context: A215991 A099592 A240922 * A144563 A175746 A179690

Adjacent sequences:  A014572 A014573 A014574 * A014576 A014577 A014578

KEYWORD

nonn,base

AUTHOR

Eric W. Weisstein

EXTENSIONS

Edited by N. J. A. Sloane, Jan 03 2009

STATUS

approved

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Last modified September 16 07:24 EDT 2014. Contains 246799 sequences.