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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 i and j have the same number of digits and the multiset of the digits of n coincides with the multiset of the digits of i and j. 18
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
Giovanni Resta, Table of n, a(n) for n = 1..10000 (terms a(1)-a(87) by R. J. Mathar and a(88)-a(1006) by Manfred Scheucher)
Manfred Scheucher, Sage Script
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
MATHEMATICA
fQ[n_] := If[OddQ@ IntegerLength@ n, False, MemberQ[Map[Sort@ Flatten@ IntegerDigits@ # &, Select[Map[{#, n/#} &, TakeWhile[Divisors@ n, # <= Sqrt@ n &]], SameQ @@ Map[IntegerLength, #] &]], Sort@ IntegerDigits@ n]]; Select[Range[10^6], fQ] (* Michael De Vlieger, Jan 27 2017 *)
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
(PARI) is_A014575(n)={my(v=vecsort(Vecsmall(Str(n)))); #v%2 && return; my( M=10^(#v\2), L=M\10); fordiv(n, d, d<L && next; d<M || return; v==vecsort(Vecsmall(Str(d, n/d))) && return(d)) \\ Twice as fast. Returns smallest factor (A048933) if vampire number, or false (empty, 0) else. - M. F. Hasler, Mar 11 2021
CROSSREFS
The following sequences are all closely related: A020342, A014575, A080718, A280928, A048936, A144563.
Sequence in context: A288921 A099592 A240922 * A144563 A175746 A291714
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Jan 03 2009
STATUS
approved

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Last modified March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)