A number in which odd and even digits alternate. more
The first 600 alternating numbers :
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
12,
14,
16,
18,
21,
23,
25,
27,
29,
30,
32,
34,
36,
38,
41,
43,
45,
47,
49,
50,
52,
54,
56,
58,
61,
63,
65,
67,
69,
70,
72,
74,
76,
78,
81,
83,
85,
87,
89,
90,
92,
94,
96,
98,
101,
103,
105,
107,
109,
121,
123,
125,
127,
129,
141,
143,
145,
147,
149,
161,
163,
165,
167,
169,
181,
183,
185,
187,
189,
210,
212,
214,
216,
218,
230,
232,
234,
236,
238,
250,
252,
254,
256,
258,
270,
272,
274,
276,
278,
290,
292,
294,
296,
298,
301,
303,
305,
307,
309,
321,
323,
325,
327,
329,
341,
343,
345,
347,
349,
361,
363,
365,
367,
369,
381,
383,
385,
387,
389,
410,
412,
414,
416,
418,
430,
432,
434,
436,
438,
450,
452,
454,
456,
458,
470,
472,
474,
476,
478,
490,
492,
494,
496,
498,
501,
503,
505,
507,
509,
521,
523,
525,
527,
529,
541,
543,
545,
547,
549,
561,
563,
565,
567,
569,
581,
583,
585,
587,
589,
610,
612,
614,
616,
618,
630,
632,
634,
636,
638,
650,
652,
654,
656,
658,
670,
672,
674,
676,
678,
690,
692,
694,
696,
698,
701,
703,
705,
707,
709,
721,
723,
725,
727,
729,
741,
743,
745,
747,
749,
761,
763,
765,
767,
769,
781,
783,
785,
787,
789,
810,
812,
814,
816,
818,
830,
832,
834,
836,
838,
850,
852,
854,
856,
858,
870,
872,
874,
876,
878,
890,
892,
894,
896,
898,
901,
903,
905,
907,
909,
921,
923,
925,
927,
929,
941,
943,
945,
947,
949,
961,
963,
965,
967,
969,
981,
983,
985,
987,
989,
1010,
1012,
1014,
1016,
1018,
1030,
1032,
1034,
1036,
1038,
1050,
1052,
1054,
1056,
1058,
1070,
1072,
1074,
1076,
1078,
1090,
1092,
1094,
1096,
1098,
1210,
1212,
1214,
1216,
1218,
1230,
1232,
1234,
1236,
1238,
1250,
1252,
1254,
1256,
1258,
1270,
1272,
1274,
1276,
1278,
1290,
1292,
1294,
1296,
1298,
1410,
1412,
1414,
1416,
1418,
1430,
1432,
1434,
1436,
1438,
1450,
1452,
1454,
1456,
1458,
1470,
1472,
1474,
1476,
1478,
1490,
1492,
1494,
1496,
1498,
1610,
1612,
1614,
1616,
1618,
1630,
1632,
1634,
1636,
1638,
1650,
1652,
1654,
1656,
1658,
1670,
1672,
1674,
1676,
1678,
1690,
1692,
1694,
1696,
1698,
1810,
1812,
1814,
1816,
1818,
1830,
1832,
1834,
1836,
1838,
1850,
1852,
1854,
1856,
1858,
1870,
1872,
1874,
1876,
1878,
1890,
1892,
1894,
1896,
1898,
2101,
2103,
2105,
2107,
2109,
2121,
2123,
2125,
2127,
2129,
2141,
2143,
2145,
2147,
2149,
2161,
2163,
2165,
2167,
2169,
2181,
2183,
2185,
2187,
2189,
2301,
2303,
2305,
2307,
2309,
2321,
2323,
2325,
2327,
2329,
2341,
2343,
2345,
2347,
2349,
2361,
2363,
2365,
2367,
2369,
2381,
2383,
2385,
2387,
2389,
2501,
2503,
2505,
2507,
2509,
2521,
2523,
2525,
2527,
2529,
2541,
2543,
2545,
2547,
2549,
2561,
2563,
2565,
2567,
2569,
2581,
2583,
2585,
2587,
2589,
2701,
2703,
2705,
2707,
2709,
2721,
2723,
2725,
2727,
2729,
2741,
2743,
2745,
2747,
2749,
2761,
2763,
2765,
2767,
2769,
2781,
2783,
2785,
2787,
2789,
2901,
2903,
2905,
2907,
2909,
2921,
2923,
2925,
2927,
2929,
2941,
2943,
2945,
2947,
2949,
2961,
2963,
2965,
2967,
2969,
2981,
2983,
2985,
2987,
2989,
3010,
3012,
3014,
3016,
3018,
3030,
3032,
3034,
3036,
3038,
3050,
3052,
3054,
3056,
3058,
3070,
3072,
3074,
3076,
3078,
3090,
3092,
3094,
3096,
3098,
3210,
3212,
3214,
3216,
3218,
3230,
3232,
3234,
3236,
3238,
3250,
3252,
3254,
3256,
3258,
3270,
3272,
3274,
3276,
3278,
3290,
3292,
3294,
3296,
3298,
3410,
3412,
3414,
3416,
3418,
3430,
3432,
3434,
3436,
3438,
3450,
3452,
3454,
3456,
3458,
3470,
3472,
3474,
3476,
3478,
3490.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 4394529 values, from 1 to 989898989).
n\r | 0 | 1 |
2 | 2034504 | 2360025 | 2 |
3 | 1464847 | 1464839 | 1464843 | 3 |
4 | 813802 | 1416015 | 1220702 | 944010 | 4 |
5 | 878905 | 878906 | 878906 | 878906 | 878906 | 5 |
6 | 678169 | 786674 | 678170 | 786678 | 678165 | 786673 | 6 |
7 | 627791 | 627792 | 627790 | 627789 | 627790 | 627789 | 627788 | 7 |
8 | 406901 | 660808 | 651041 | 472005 | 406901 | 755207 | 569661 | 472005 | 8 |
9 | 490598 | 485964 | 490317 | 486771 | 489084 | 488281 | 487478 | 489791 | 486245 | 9 |
10 | 406900 | 472005 | 406901 | 472005 | 406901 | 472005 | 406901 | 472005 | 406901 | 472005 | 10 |
11 | 427280 | 374177 | 420325 | 384872 | 406756 | 400215 | 390883 | 415331 | 377749 | 425419 | 371522 |
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.