# Three-Fanged Vampires

Hans Havermann hahaj at rogers.com
Thu Oct 10 16:37:13 CEST 2002

```A048937 was one of the five one-term sequences that I culled from the
Integer-Sequence database recently:

%I A048937
%S A048937 13078260
%N A048937 Vampire numbers having exactly three distinct pairs of fangs.
%D A048937 C. A. Pickover, "Vampire Numbers." Ch. 30 in Keys to
Infinity. New York: Wiley, pp. 227-231, 1995.
%H A048937 E. W. Weisstein, <a
section of The World of\
Mathematics.</a>
%Y A048937 Cf. A014575, A048933, ..., A048939.
%K A048937 nonn,more,bref
%O A048937 1,1
%A A048937 Eric W. Weisstein (eric at weisstein.com)

A web-search came up with Walter Schneider's
http://wschnei.de/digit-related-numbers/vampire.html in which he stated
"The search for the 12 digit vampire numbers was done at 17th February
2002 and lasted 6 hours and 30 minutes on a Pentium III with 550 MHz."
He then summarizes his findings in a little table which indicated 15
twelve-digit vampire numbers "with 3 different pairs of fangs".

> the 15 examples are:
>
> 068431579920 = 197802 x 345960
> 068431579920 = 172980 x 395604
> 068431579920 = 190278 x 359640
>
> 097242563880 = 202860 x 479358
> 097242563880 = 239085 x 406728
> 097242563880 = 237258 x 409860
>
> 107650322640 = 153204 x 702660
> 107650322640 = 140532 x 766020
> 107650322640 = 200760 x 536214
>
> 113024597400 = 257400 x 439101
> 113024597400 = 152100 x 743094
> 113024597400 = 125100 x 903474
>
> 119634515208 = 285513 x 419016
> 119634515208 = 234156 x 510918
> 119634515208 = 195351 x 612408
>
> 134549287600 = 145700 x 923468
> 134549287600 = 138650 x 970424
> 134549287600 = 182900 x 735644
>
> 135173486250 = 361185 x 374250
> 135173486250 = 164175 x 823350
> 135173486250 = 328350 x 411675
>
> 138130447950 = 140415 x 983730
> 138130447950 = 308913 x 447150
> 138130447950 = 330891 x 417450
>
> 146083269717 = 204687 x 713691
> 146083269717 = 167409 x 872613
> 146083269717 = 237897 x 614061
>
> 150967233648 = 163548 x 923076
> 150967233648 = 367983 x 410256
> 150967233648 = 327096 x 461538
>
> 216315684000 = 316251 x 684000
> 216315684000 = 421668 x 513000
> 216315684000 = 351000 x 616284
>
> 221089445500 = 225500 x 980441
> 221089445500 = 440198 x 502250
> 221089445500 = 441980 x 500225
>
> 315987404670 = 446859 x 707130
> 315987404670 = 348705 x 906174
> 315987404670 = 453087 x 697410
>
> 463997983680 = 469938 x 987360
> 463997983680 = 493680 x 939876
> 463997983680 = 478380 x 969936
>
> 472812953760 = 671328 x 704295
> 472812953760 = 657342 x 719280
> 472812953760 = 629370 x 751248

Now I know there might be issues with the initial-zero and the
terminal-multiple-zero entries but, once these are resolved, there
should be a few more terms in A048937.

```