A number whose digits are in strict ascending order. more
The metadromes up to 10
15 :
1,
2,
3,
4,
5,
6,
7,
8,
9,
12,
13,
14,
15,
16,
17,
18,
19,
23,
24,
25,
26,
27,
28,
29,
34,
35,
36,
37,
38,
39,
45,
46,
47,
48,
49,
56,
57,
58,
59,
67,
68,
69,
78,
79,
89,
123,
124,
125,
126,
127,
128,
129,
134,
135,
136,
137,
138,
139,
145,
146,
147,
148,
149,
156,
157,
158,
159,
167,
168,
169,
178,
179,
189,
234,
235,
236,
237,
238,
239,
245,
246,
247,
248,
249,
256,
257,
258,
259,
267,
268,
269,
278,
279,
289,
345,
346,
347,
348,
349,
356,
357,
358,
359,
367,
368,
369,
378,
379,
389,
456,
457,
458,
459,
467,
468,
469,
478,
479,
489,
567,
568,
569,
578,
579,
589,
678,
679,
689,
789,
1234,
1235,
1236,
1237,
1238,
1239,
1245,
1246,
1247,
1248,
1249,
1256,
1257,
1258,
1259,
1267,
1268,
1269,
1278,
1279,
1289,
1345,
1346,
1347,
1348,
1349,
1356,
1357,
1358,
1359,
1367,
1368,
1369,
1378,
1379,
1389,
1456,
1457,
1458,
1459,
1467,
1468,
1469,
1478,
1479,
1489,
1567,
1568,
1569,
1578,
1579,
1589,
1678,
1679,
1689,
1789,
2345,
2346,
2347,
2348,
2349,
2356,
2357,
2358,
2359,
2367,
2368,
2369,
2378,
2379,
2389,
2456,
2457,
2458,
2459,
2467,
2468,
2469,
2478,
2479,
2489,
2567,
2568,
2569,
2578,
2579,
2589,
2678,
2679,
2689,
2789,
3456,
3457,
3458,
3459,
3467,
3468,
3469,
3478,
3479,
3489,
3567,
3568,
3569,
3578,
3579,
3589,
3678,
3679,
3689,
3789,
4567,
4568,
4569,
4578,
4579,
4589,
4678,
4679,
4689,
4789,
5678,
5679,
5689,
5789,
6789,
12345,
12346,
12347,
12348,
12349,
12356,
12357,
12358,
12359,
12367,
12368,
12369,
12378,
12379,
12389,
12456,
12457,
12458,
12459,
12467,
12468,
12469,
12478,
12479,
12489,
12567,
12568,
12569,
12578,
12579,
12589,
12678,
12679,
12689,
12789,
13456,
13457,
13458,
13459,
13467,
13468,
13469,
13478,
13479,
13489,
13567,
13568,
13569,
13578,
13579,
13589,
13678,
13679,
13689,
13789,
14567,
14568,
14569,
14578,
14579,
14589,
14678,
14679,
14689,
14789,
15678,
15679,
15689,
15789,
16789,
23456,
23457,
23458,
23459,
23467,
23468,
23469,
23478,
23479,
23489,
23567,
23568,
23569,
23578,
23579,
23589,
23678,
23679,
23689,
23789,
24567,
24568,
24569,
24578,
24579,
24589,
24678,
24679,
24689,
24789,
25678,
25679,
25689,
25789,
26789,
34567,
34568,
34569,
34578,
34579,
34589,
34678,
34679,
34689,
34789,
35678,
35679,
35689,
35789,
36789,
45678,
45679,
45689,
45789,
46789,
56789,
123456,
123457,
123458,
123459,
123467,
123468,
123469,
123478,
123479,
123489,
123567,
123568,
123569,
123578,
123579,
123589,
123678,
123679,
123689,
123789,
124567,
124568,
124569,
124578,
124579,
124589,
124678,
124679,
124689,
124789,
125678,
125679,
125689,
125789,
126789,
134567,
134568,
134569,
134578,
134579,
134589,
134678,
134679,
134689,
134789,
135678,
135679,
135689,
135789,
136789,
145678,
145679,
145689,
145789,
146789,
156789,
234567,
234568,
234569,
234578,
234579,
234589,
234678,
234679,
234689,
234789,
235678,
235679,
235689,
235789,
236789,
245678,
245679,
245689,
245789,
246789,
256789,
345678,
345679,
345689,
345789,
346789,
356789,
456789,
1234567,
1234568,
1234569,
1234578,
1234579,
1234589,
1234678,
1234679,
1234689,
1234789,
1235678,
1235679,
1235689,
1235789,
1236789,
1245678,
1245679,
1245689,
1245789,
1246789,
1256789,
1345678,
1345679,
1345689,
1345789,
1346789,
1356789,
1456789,
2345678,
2345679,
2345689,
2345789,
2346789,
2356789,
2456789,
3456789,
12345678,
12345679,
12345689,
12345789,
12346789,
12356789,
12456789,
13456789,
23456789,
123456789.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 511 values, from 1 to 123456789).
n\r | 0 | 1 |
2 | 170 | 341 | 2 |
3 | 175 | 168 | 168 | 3 |
4 | 68 | 205 | 102 | 136 | 4 |
5 | 16 | 33 | 66 | 132 | 264 | 5 |
6 | 59 | 114 | 57 | 116 | 54 | 111 | 6 |
7 | 72 | 73 | 73 | 73 | 73 | 73 | 74 | 7 |
8 | 40 | 89 | 44 | 56 | 28 | 116 | 58 | 80 | 8 |
9 | 59 | 56 | 56 | 58 | 56 | 56 | 58 | 56 | 56 | 9 |
10 | 0 | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 10 |
11 | 0 | 9 | 36 | 84 | 126 | 126 | 84 | 36 | 9 | 1 | 0 |
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.