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 |
2 | 81772 | 30065 | 2 |
3 | 55834 | 56003 | 0 | 3 |
4 | 54135 | 14439 | 27637 | 15626 | 4 |
5 | 49770 | 13953 | 14942 | 17597 | 15575 | 5 |
6 | 40816 | 15047 | 0 | 15018 | 40956 | 0 | 6 |
7 | 29933 | 13732 | 13531 | 13642 | 13691 | 13615 | 13693 | 7 |
8 | 34201 | 7314 | 13526 | 7793 | 19934 | 7125 | 14111 | 7833 | 8 |
9 | 55834 | 0 | 0 | 0 | 56003 | 0 | 0 | 0 | 0 | 9 |
10 | 36253 | 2901 | 10074 | 4350 | 11146 | 13517 | 11052 | 4868 | 13247 | 4429 | 10 |
11 | 19392 | 9353 | 9409 | 9113 | 9279 | 9224 | 9174 | 9431 | 9157 | 9079 | 9226 |
A pictorial representation of the table above
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.