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vampire numbers
A number n of 2k digits that is the product of two k-digit numbers which together have the same digits of n. more

The first 600 vampire numbers :
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, 129775, 131242, 132430, 133245, 134725, 135828, 135837, 136525, 136948, 140350, 145314, 146137, 146952, 150300, 152608, 152685, 153436, 156240, 156289, 156915, 162976, 163944, 172822, 173250, 174370, 175329, 180225, 180297, 182250, 182650, 186624, 190260, 192150, 193257, 193945, 197725, 201852, 205785, 211896, 213466, 215860, 216733, 217638, 218488, 226498, 226872, 229648, 233896, 241564, 245182, 251896, 253750, 254740, 260338, 262984, 263074, 284598, 284760, 286416, 296320, 304717, 312475, 312975, 315594, 315900, 319059, 319536, 326452, 329346, 329656, 336550, 336960, 338296, 341653, 346968, 361989, 362992, 365638, 368550, 369189, 371893, 378400, 378418, 378450, 384912, 386415, 392566, 404968, 414895, 416650, 416988, 428980, 429664, 447916, 456840, 457600, 458640, 475380, 486720, 489159, 489955, 498550, 516879, 529672, 536539, 538650, 559188, 567648, 568750, 629680, 638950, 673920, 679500, 729688, 736695, 738468, 769792, 789250, 789525, 792585, 794088, 809919, 809964, 815958, 829696, 841995, 939658, 10025010, 10042510, 10052010, 10052064, 10081260, 10102252, 10124352, 10124757, 10127475, 10128235, 10129900, 10133788, 10134985, 10149750, 10165680, 10165815, 10166350, 10173820, 10185934, 10192248, 10195794, 10205100, 10205370, 10217493, 10219680, 10229845, 10233054, 10237864, 10245550, 10245820, 10248925, 10250460, 10254100, 10255000, 10257790, 10269504, 10269598, 10291779, 10293966, 10294200, 10294695, 10311966, 10323225, 10349527, 10371649, 10391746, 10396800, 10402600, 10417167, 10423530, 10429753, 10434226, 10437678, 10461784, 10462090, 10467792, 10471162, 10471293, 10502100, 10507500, 10511694, 10518678, 10522350, 10524208, 10525000, 10526400, 10558368, 10571080, 10572300, 10591398, 10592482, 10604277, 10619145, 10642540, 10656432, 10657480, 10665720, 10671417, 10671660, 10687513, 10696824, 10699744, 10716300, 10723185, 10731609, 10732306, 10732900, 10734192, 10742868, 10767568, 10772190, 10792390, 10796674, 10801350, 10821600, 10832850, 10835370, 10851939, 10886400, 10905250, 10932754, 10935436, 10958157, 10965595, 11053714, 11059164, 11064280, 11074657, 11074905, 11085304, 11147836, 11148520, 11158735, 11165728, 11185762, 11187360, 11246800, 11246890, 11254945, 11259000, 11272356, 11281648, 11286193, 11293744, 11306857, 11330865, 11344860, 11345229, 11364138, 11368026, 11369533, 11378169, 11388762, 11391250, 11417805, 11420923, 11426800, 11435985, 11438266, 11447428, 11447860, 11453481, 11472628, 11474788, 11479230, 11506770, 11515383, 11522250, 11525490, 11526844, 11529216, 11536875, 11541816, 11545218, 11557323, 11559960, 11564280, 11567205, 11569900, 11572596, 11575435, 11576268, 11602926, 11607250, 11608272, 11609950, 11632896, 11643088, 11643282, 11647800, 11648952, 11657835, 11672590, 11675668, 11677140, 11680767, 11682468, 11683512, 11689744, 11690532, 11692228, 11692800, 11697835, 11712757, 11722657, 11726820, 11727625, 11728615, 11728786, 11736652, 11753874, 11756250, 11765596, 11766892, 11772540, 11786350, 11790166, 11794684, 11796160, 11803482, 11815650, 11823997, 11830315, 11833645, 11844054, 11844832, 11848000, 11850394, 11857500, 11867467, 11874550, 11876602, 11883613, 11887524, 11898535, 11908215, 11920468, 11920657, 11922484, 11924703, 11925540, 11926134, 11926728, 11929918, 11930170, 11948310, 11952292, 11952360, 11954619, 11957512, 11964582, 11970256, 11976178, 11982348, 12006000, 12015396, 12023550, 12041964, 12045982, 12052048, 12054060, 12054820, 12055950, 12056850, 12060027, 12081960, 12083575, 12083706, 12085650, 12095568, 12097147, 12097350, 12098646, 12128935, 12129754, 12142597, 12145693, 12157600, 12159720, 12166942, 12169480, 12181500, 12195760, 12199752, 12210588, 12213585, 12238776, 12245395, 12247686, 12254620, 12259345, 12261582, 12271545, 12274515, 12274600, 12276400, 12276544, 12289644, 12295480, 12296740, 12303837, 12308436, 12310938, 12328960, 12338046, 12340368, 12342555, 12347680, 12353800, 12363840, 12367260, 12371904, 12373690, 12374712, 12383059, 12384000, 12387735, 12406770, 12408385, 12408430, 12417588, 12417993, 12419775, 12421066, 12439129, 12447184, 12448800, 12451927, 12452080, 12453012, 12454200, 12455118, 12459640, 12463960, 12467052, 12475606, 12483576, 12484057, 12485115, 12488760, 12489471, 12492864, 12495280, 12497800, 12504960, 12505000, 12509640, 12519846, 12524008, 12526290, 12531834, 12536320, 12550018, 12550050, 12552813, 12557290, 12558100, 12559095, 12568270, 12574845, 12577617, 12578449, 12578764, 12579214, 12586392, 12594712, 12595000, 12597930, 12600297, 12600324, 12608743, 12613990, 12618850, 12620790, 12634560, 12636040, 12640095, 12640860, 12645360, 12652024, 12654513, 12665475, 12678250, 12683385, 12684924, 12693420, 12693928, 12697740, 12698334, 12715762, 12716586, 12717396, 12735895, 12741700, 12746515, 12746650, 12752640, 12752860, 12754075, 12759250, 12762000, 12775945, 12778155, 12805240, 12805384, 12810735, 12827650, 12832524, 12833590, 12843000, 12851586, 12853840, 12854488, 12859150, 12873294, 12883486, 12883540, 12885147, 12893760, 12894547, 12916750, 12941037, 12943548, 12951400, 12955000, 12965035, 12965175, 12966480, 12993525, 13002462, 13024480, 13024557, 13024872, 13025650, 13029565, 13041180, 13041909, 13042849, 13062460, 13062780, 13078260, 13086540, 13104954, 13104994, 13130685, 13140292, 13142038, 13168575, 13204125, 13204750, 13204930, 13208670, 13225518, 13230369, 13230945, 13234864, 13241250, 13241974, 13248540, 13253764, 13257760, 13261500, 13264150, 13268772, 13269258.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 111837 values, from 1260 to 9953948970).

n\r 0  1 
28177230065 2 
355834560030 3 
454135144392763715626 4 
54977013953149421759715575 5 
64081615047015018409560 6 
729933137321353113642136911361513693 7 
8342017314135267793199347125141117833 8 
955834000560030000 9 
103625329011007443501114613517110524868132474429 10 
11193929353940991139279922491749431915790799226

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.