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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) Ely Golden, Sympy program for generating vampire numbers (definition 2) 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

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Last modified August 7 01:19 EDT 2024. Contains 375002 sequences. (Running on oeis4.)