A number n whose digits can be separated into two numbers a and b such that n divided by b gives a as remainder. more
The first 600 modest numbers :
13,
19,
23,
26,
29,
39,
46,
49,
59,
69,
79,
89,
103,
109,
111,
133,
199,
203,
206,
209,
211,
218,
222,
233,
266,
299,
309,
311,
327,
333,
399,
406,
409,
411,
412,
418,
422,
433,
436,
444,
466,
499,
509,
511,
515,
533,
545,
555,
599,
609,
611,
618,
622,
627,
633,
654,
666,
699,
709,
711,
721,
733,
763,
777,
799,
809,
811,
812,
818,
822,
824,
833,
836,
844,
866,
872,
888,
899,
911,
927,
933,
981,
999,
1003,
1009,
1011,
1015,
1018,
1022,
1027,
1030,
1033,
1037,
1045,
1055,
1066,
1090,
1099,
1111,
1133,
1199,
1218,
1222,
1227,
1233,
1236,
1244,
1254,
1266,
1299,
1333,
1339,
1399,
1418,
1421,
1422,
1433,
1442,
1463,
1466,
1477,
1499,
1527,
1533,
1545,
1555,
1599,
1618,
1622,
1624,
1633,
1636,
1644,
1648,
1666,
1672,
1688,
1699,
1733,
1751,
1799,
1822,
1827,
1833,
1854,
1866,
1881,
1899,
1933,
1957,
1999,
2003,
2006,
2009,
2018,
2022,
2027,
2030,
2033,
2036,
2037,
2044,
2045,
2054,
2055,
2060,
2066,
2074,
2090,
2099,
2111,
2127,
2133,
2163,
2177,
2199,
2222,
2233,
2266,
2299,
2333,
2369,
2399,
2427,
2433,
2436,
2444,
2454,
2466,
2472,
2488,
2499,
2533,
2545,
2555,
2575,
2599,
2633,
2639,
2666,
2678,
2699,
2733,
2781,
2799,
2833,
2836,
2842,
2844,
2863,
2866,
2877,
2884,
2899,
2933,
2987,
2999,
3009,
3027,
3033,
3037,
3045,
3054,
3055,
3066,
3081,
3090,
3099,
3111,
3133,
3193,
3199,
3233,
3236,
3244,
3248,
3266,
3272,
3288,
3296,
3299,
3333,
3399,
3451,
3466,
3499,
3545,
3555,
3563,
3577,
3599,
3644,
3654,
3666,
3681,
3699,
3799,
3857,
3866,
3899,
3999,
4006,
4009,
4012,
4018,
4027,
4036,
4037,
4044,
4045,
4054,
4055,
4060,
4066,
4072,
4074,
4088,
4090,
4099,
4108,
4111,
4148,
4199,
4222,
4254,
4263,
4266,
4277,
4299,
4333,
4399,
4444,
4466,
4499,
4555,
4581,
4599,
4666,
4669,
4699,
4799,
4854,
4866,
4872,
4888,
4899,
4963,
4977,
4999,
5009,
5015,
5027,
5037,
5045,
5055,
5066,
5075,
5090,
5099,
5111,
5135,
5185,
5199,
5266,
5278,
5299,
5333,
5399,
5466,
5481,
5499,
5555,
5599,
5663,
5666,
5672,
5677,
5684,
5688,
5699,
5799,
5866,
5887,
5899,
5999,
6009,
6018,
6027,
6037,
6054,
6066,
6074,
6081,
6090,
6099,
6111,
6162,
6199,
6222,
6266,
6293,
6299,
6333,
6377,
6381,
6399,
6466,
6472,
6488,
6496,
6499,
6599,
6666,
6699,
6799,
6899,
6999,
7009,
7021,
7027,
7037,
7063,
7077,
7090,
7099,
7111,
7189,
7199,
7259,
7281,
7288,
7299,
7333,
7399,
7499,
7599,
7699,
7777,
7799,
7899,
7999,
8009,
8012,
8018,
8024,
8027,
8036,
8037,
8054,
8072,
8074,
8088,
8090,
8099,
8108,
8111,
8148,
8199,
8216,
8222,
8296,
8299,
8333,
8399,
8444,
8499,
8599,
8666,
8699,
8799,
8888,
8899,
8999,
9027,
9037,
9081,
9099,
9111,
9199,
9243,
9299,
9333,
9399,
9499,
9599,
9699,
9799,
9899,
9999,
10003,
10009,
10011,
10015,
10018,
10027,
10030,
10033,
10037,
10045,
10054,
10074,
10090,
10099,
10101,
10111,
10135,
10185,
10222,
10270,
10303,
10333,
10370,
10555,
10666,
10909,
10999,
11027,
11033,
11037,
11099,
11111,
11297,
11333,
11407,
11999,
12018,
12027,
12036,
12037,
12054,
12074,
12081,
12108,
12111,
12148,
12162,
12222,
12324,
12333,
12444,
12666,
12999,
13027,
13037,
13039,
13111,
13117,
13333,
13351,
13481,
13999,
14018,
14021,
14027,
14037,
14042,
14054,
14063,
14074,
14111,
14126,
14189,
14222,
14259,
14333,
14378,
14518,
14666,
14777,
14999,
15027,
15037,
15045,
15081,
15111,
15135,
15185,
15333,
15405,
15555,
15999,
16018,
16024,
16027,
16036,
16037,
16048,
16054,
16072,
16074,
16108,
16111,
16144,
16148,
16216,
16222,
16296,
16333,
16432,
16444,
16592,
16666,
16888,
16999,
17027,
17037,
17051,
17111,
17153,
17333,
17459,
17629,
17999,
18027,
18037,
18054,
18074,
18081,
18111,
18162,
18222,
18243,
18333,
18486,
18666,
18999,
19027,
19037,
19057,
19111,
19171,
19333,
19513,
19703,
19999,
20003,
20006,
20009,
20011,
20018.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 894499 values, from 13 to 1999999999).
n\r | 0 | 1 |
2 | 414379 | 480120 | 2 |
3 | 343592 | 275649 | 275258 | 3 |
4 | 191973 | 230186 | 222406 | 249934 | 4 |
5 | 148755 | 184648 | 176378 | 186679 | 198039 | 5 |
6 | 158422 | 147528 | 127836 | 185170 | 128121 | 147422 | 6 |
7 | 197033 | 116279 | 116290 | 116285 | 116273 | 116134 | 116205 | 7 |
8 | 89990 | 107159 | 112567 | 108468 | 101983 | 123027 | 109839 | 141466 | 8 |
9 | 126448 | 91963 | 91675 | 108548 | 91861 | 91799 | 108596 | 91825 | 91784 | 9 |
10 | 67698 | 93685 | 88470 | 103952 | 84521 | 81057 | 90963 | 87908 | 82727 | 113518 | 10 |
11 | 111231 | 78349 | 78262 | 78353 | 78434 | 78389 | 78304 | 78331 | 78392 | 78122 | 78332 |
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.