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A014575
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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.
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14
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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
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OFFSET
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1,1
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COMMENTS
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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]
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REFERENCES
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C. A. Pickover, "Vampire Numbers." Ch. 30 in Keys to Infinity. New York: Wiley, pp. 227-231, 1995.
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..87
Eric Weisstein's World of Mathematics, Vampire Number.
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EXAMPLE
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1260 = 21*60, 1395 = 15*93, 1435 = 35*41, 1530 = 30*51, etc.
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MAPLE
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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
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PROG
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(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
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CROSSREFS
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The following sequences are all closely related: A020342, A014575, A080718, A048936, A144563.
Cf. A048933, A048934, ..., A048939.
Sequence in context: A211773 A215991 A099592 * A144563 A175746 A179690
Adjacent sequences: A014572 A014573 A014574 * A014576 A014577 A014578
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KEYWORD
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nonn,base
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Edited by N. J. A. Sloane, Jan 03 2009
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STATUS
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approved
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