cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

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]

Examples

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

References

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

Links

Crossrefs

The following sequences are all closely related: A020342, A014575, A080718, A280928, A048936, A144563.
Cf. A048933, A048934, A048935, A048936, A048937, A048938, A048939.

Programs

  • 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 *)
  • 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, dA048933) if vampire number, or false (empty, 0) else. - M. F. Hasler, Mar 11 2021

Extensions

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

A048936 Subset of vampire numbers A014575 having exactly two representations of the desired form.

Original entry on oeis.org

125460, 11930170, 12054060, 12417993, 12600324, 12827650, 13002462, 22569480, 23287176, 26198073, 26373600, 26839800, 46847920, 61360780, 1001795850, 1013265360, 1017509850, 1018172470, 1044022896, 1047395790
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Examples

			125460 = 204*615 = 246*510.
11930170 = 1301*9170 = 1310*9107.
12054060 = 2004*6015 = 2406*5010.

References

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

Links

Crossrefs

Closely related: A020342, A014575, A080718, A280928, A144563.
Cf. A014575, A048933, ..., A048939.

Extensions

Edited by N. J. A. Sloane, Jan 03 2009
Name edited by M. F. Hasler, Mar 11 2021

A048939 10-digit vampire numbers (definition 2).

Original entry on oeis.org

1000174288, 1000191991, 1000198206, 1000250010, 1000407528, 1000425010, 1000520010, 1000520064, 1000812510, 1001020252, 1001127442, 1001139282, 1001147422, 1001193790, 1001240352, 1001244420, 1001249680, 1001288794
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

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

Links

Crossrefs

Cf. A014575, A048933, ..., A048938.

A048938 8-digit vampire numbers (definition 2).

Original entry on oeis.org

10025010, 10042510, 10052010, 10052064, 10081260, 10102252, 10124352, 10124757, 10127475, 10128235, 10129900, 10133788, 10134985, 10149750, 10165680, 10165815, 10166350, 10173820, 10185934, 10192248, 10195794
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

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

Links

Crossrefs

Cf. A014575, A048933, ..., A048936.

A048934 Largest factor i of any factorization used in the definition of A014575(n).

Original entry on oeis.org

60, 93, 41, 51, 87, 81, 86, 510, 401, 501, 516, 705, 801, 701, 761, 725, 701, 840, 600, 534, 443, 824, 543, 615, 500, 627, 486, 926, 725, 422, 410, 423, 425, 588, 387, 635, 938, 401, 414, 461, 942, 501, 608, 585, 431, 651, 581, 951, 926, 414, 782, 750, 470
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

References

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

Links

Crossrefs

Cf. A014575, A048933, ..., A048939.

Extensions

Edited by N. J. A. Sloane, Jan 03 2009
Terms a(25) and beyond from b-file by Andrew Howroyd, Feb 05 2018

A048937 Numbers n with an even number of digits, n = d_1 d_2 ... d_n, such that there are exactly three ways to partition the digits into two groups of size n/2, say f_1 ... f_{n/2} and g_1 ... g_{n/2}, such that n = f_1 ... f_{n/2} * g_1 ... g_{n/2}.

Original entry on oeis.org

13078260, 107650322640, 113024597400, 119634515208, 134549287600, 135173486250, 138130447950, 146083269717, 150967233648, 216315684000, 221089445500, 315987404670, 463997983680, 472812953760, 10174695862032, 10178463985200, 10185571893960, 10476754939728, 10624657891320
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

f_{n/2} and g_{n/2} may not both be zero.
Vampire numbers (definition 2) having exactly three distinct pairs of fangs.

Examples

			13078260 = 1620*8073 = 1863*7020 = 2070*6318; 107650322640 = 153204*702660 = 140532*766020 = 200760*536214.

References

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

Links

Crossrefs

Cf. A014575, A048933, ..., A048939.

Extensions

More terms found by Walter Schneider, Feb 11 2002 and communicated by Hans Havermann, Oct 10 2002
More terms from Jens Kruse Andersen, Dec 01 2002
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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