A number whose representation in base b contains all the digits from 0 to b-1. more
The first 600 pandigital numbers :
2,
11,
15,
19,
21,
75,
78,
99,
108,
114,
120,
135,
141,
147,
156,
177,
180,
198,
201,
210,
216,
225,
228,
694,
698,
714,
722,
738,
742,
894,
898,
954,
970,
978,
990,
1014,
1022,
1054,
1070,
1102,
1110,
1138,
1142,
1178,
1190,
1202,
1210,
1294,
1298,
1334,
1346,
1358,
1366,
1394,
1398,
1454,
1470,
1478,
1490,
1634,
1646,
1654,
1670,
1726,
1730,
1758,
1766,
1778,
1790,
1826,
1830,
1914,
1922,
1934,
1946,
1982,
1986,
2014,
2022,
2054,
2070,
2102,
2110,
2134,
2146,
2154,
2170,
2226,
2230,
2382,
2386,
2402,
2410,
2426,
2430,
2538,
2542,
2558,
2566,
2582,
2586,
2638,
2642,
2678,
2690,
2702,
2710,
2758,
2766,
2778,
2790,
2826,
2830,
2882,
2886,
2902,
2910,
2926,
2930,
8345,
8350,
8375,
8385,
8410,
8415,
8525,
8530,
8585,
8600,
8620,
8630,
8735,
8745,
8765,
8780,
8835,
8840,
8950,
8955,
8980,
8990,
9015,
9020,
10505,
10510,
10535,
10545,
10570,
10575,
11045,
11050,
11165,
11190,
11200,
11220,
11255,
11265,
11345,
11370,
11415,
11430,
11470,
11475,
11560,
11580,
11595,
11610,
11765,
11770,
11825,
11840,
11860,
11870,
12125,
12130,
12245,
12270,
12280,
12300,
12545,
12560,
12605,
12630,
12710,
12720,
12760,
12770,
12820,
12840,
12890,
12900,
13055,
13065,
13085,
13100,
13155,
13160,
13415,
13425,
13505,
13530,
13575,
13590,
13625,
13640,
13685,
13710,
13790,
13800,
14055,
14060,
14115,
14130,
14150,
14160,
14350,
14355,
14380,
14390,
14415,
14420,
14710,
14715,
14800,
14820,
14835,
14850,
14920,
14930,
14980,
15000,
15050,
15060,
15135,
15140,
15195,
15210,
15230,
15240,
15905,
15910,
15935,
15945,
15970,
15975,
16265,
16270,
16355,
16375,
16390,
16405,
16475,
16485,
16535,
16555,
16605,
16615,
16690,
16695,
16750,
16765,
16785,
16795,
16985,
16990,
17015,
17025,
17050,
17055,
17525,
17530,
17645,
17670,
17680,
17700,
17735,
17745,
17825,
17850,
17895,
17910,
17950,
17955,
18040,
18060,
18075,
18090,
19505,
19510,
19595,
19615,
19630,
19645,
19685,
19690,
19805,
19830,
19840,
19860,
20315,
20335,
20345,
20370,
20485,
20490,
20530,
20545,
20560,
20580,
20665,
20670,
20795,
20805,
20855,
20875,
20925,
20935,
20975,
20985,
21065,
21090,
21135,
21150,
21395,
21415,
21425,
21450,
21565,
21570,
21825,
21835,
21855,
21870,
21925,
21930,
22090,
22095,
22150,
22165,
22185,
22195,
22270,
22275,
22360,
22380,
22395,
22410,
22690,
22705,
22720,
22740,
22825,
22830,
22905,
22915,
22935,
22950,
23005,
23010,
23645,
23650,
23705,
23720,
23740,
23750,
23825,
23830,
23915,
23935,
23950,
23965,
24245,
24260,
24275,
24295,
24380,
24385,
24460,
24470,
24490,
24505,
24560,
24565,
24725,
24730,
24785,
24800,
24820,
24830,
25085,
25090,
25205,
25230,
25240,
25260,
25505,
25520,
25565,
25590,
25670,
25680,
25720,
25730,
25780,
25800,
25850,
25860,
25985,
25990,
26075,
26095,
26110,
26125,
26165,
26170,
26285,
26310,
26320,
26340,
26795,
26815,
26825,
26850,
26965,
26970,
27010,
27025,
27040,
27060,
27145,
27150,
28565,
28580,
28595,
28615,
28700,
28705,
28745,
28760,
28805,
28830,
28910,
28920,
28955,
28975,
28985,
29010,
29125,
29130,
29600,
29605,
29630,
29640,
29665,
29670,
29860,
29870,
29890,
29905,
29960,
29965,
30040,
30050,
30100,
30120,
30170,
30180,
30250,
30265,
30280,
30300,
30385,
30390,
30680,
30685,
30710,
30720,
30745,
30750,
31415,
31425,
31445,
31460,
31515,
31520,
31595,
31605,
31655,
31675,
31725,
31735,
31805,
31820,
31835,
31855,
31940,
31945,
32235,
32240,
32265,
32275,
32300,
32305,
32495,
32505,
32525,
32540,
32595,
32600,
32855,
32865,
32945,
32970,
33015,
33030,
33065,
33080,
33125,
33150,
33230,
33240,
33495,
33500,
33555,
33570,
33590,
33600,
33755,
33765,
33815,
33835,
33885,
33895,
33935,
33945,
34025,
34050,
34095,
34110,
34355,
34375,
34385,
34410,
34525,
34530,
34785,
34795,
34815,
34830,
34885,
34890,
35045,
35060,
35075,
35095,
35180,
35185,
35225,
35240,
35285,
35310,
35390,
35400,
35435,
35455,
35465,
35490,
35605,
35610,
36080,
36085,
36110,
36120,
36145,
36150,
37635,
37640,
37665,
37675,
37700,
37705,
37815,
37820,
37875,
37890,
37910,
37920,
38025,
38035,
38055,
38070,
38125,
38130,
38240,
38245,
38270,
38280,
38305,
38310,
39190.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 3628799 values, from 2 to 9876543210).
n\r | 0 | 1 |
2 | 1994099 | 1634700 | 2 |
3 | 3392472 | 118013 | 118314 | 3 |
4 | 1138470 | 837305 | 855629 | 797395 | 4 |
5 | 758019 | 717012 | 716929 | 716990 | 719849 | 5 |
6 | 1769810 | 6073 | 112349 | 1622662 | 111940 | 5965 | 6 |
7 | 547892 | 513641 | 513259 | 512513 | 513651 | 514310 | 513533 | 7 |
8 | 408318 | 418663 | 427799 | 398627 | 730152 | 418642 | 427830 | 398768 | 8 |
9 | 3311739 | 39382 | 39405 | 40508 | 39256 | 39531 | 40225 | 39375 | 39378 | 9 |
10 | 430803 | 326960 | 390043 | 326808 | 393019 | 327216 | 390052 | 326886 | 390182 | 326830 | 10 |
11 | 318285 | 329636 | 332615 | 329759 | 332563 | 329364 | 332749 | 329395 | 332311 | 329903 | 332219 |
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.