A number which survives a sieving process similar (but different) to the Sieve of Eratosthenes for primes more
The first 600 lucky numbers :
1,
3,
7,
9,
13,
15,
21,
25,
31,
33,
37,
43,
49,
51,
63,
67,
69,
73,
75,
79,
87,
93,
99,
105,
111,
115,
127,
129,
133,
135,
141,
151,
159,
163,
169,
171,
189,
193,
195,
201,
205,
211,
219,
223,
231,
235,
237,
241,
259,
261,
267,
273,
283,
285,
289,
297,
303,
307,
319,
321,
327,
331,
339,
349,
357,
361,
367,
385,
391,
393,
399,
409,
415,
421,
427,
429,
433,
451,
463,
475,
477,
483,
487,
489,
495,
511,
517,
519,
529,
535,
537,
541,
553,
559,
577,
579,
583,
591,
601,
613,
615,
619,
621,
631,
639,
643,
645,
651,
655,
673,
679,
685,
693,
699,
717,
723,
727,
729,
735,
739,
741,
745,
769,
777,
781,
787,
801,
805,
819,
823,
831,
841,
855,
867,
873,
883,
885,
895,
897,
903,
925,
927,
931,
933,
937,
957,
961,
975,
979,
981,
991,
993,
997,
1009,
1011,
1021,
1023,
1029,
1039,
1041,
1053,
1057,
1087,
1093,
1095,
1101,
1105,
1107,
1117,
1123,
1147,
1155,
1167,
1179,
1183,
1189,
1197,
1201,
1203,
1209,
1219,
1231,
1233,
1245,
1249,
1251,
1261,
1263,
1275,
1281,
1285,
1291,
1303,
1309,
1323,
1329,
1339,
1357,
1365,
1369,
1387,
1389,
1395,
1401,
1417,
1419,
1435,
1441,
1455,
1459,
1471,
1473,
1485,
1491,
1495,
1497,
1501,
1503,
1519,
1533,
1543,
1545,
1563,
1567,
1575,
1579,
1585,
1587,
1597,
1599,
1611,
1639,
1641,
1645,
1659,
1663,
1675,
1693,
1701,
1705,
1711,
1723,
1731,
1737,
1749,
1765,
1767,
1771,
1773,
1777,
1797,
1801,
1809,
1819,
1827,
1831,
1833,
1839,
1857,
1869,
1879,
1893,
1899,
1915,
1921,
1923,
1933,
1941,
1945,
1959,
1963,
1965,
1977,
1983,
1987,
1995,
2001,
2019,
2023,
2031,
2053,
2059,
2065,
2067,
2079,
2083,
2085,
2095,
2113,
2115,
2121,
2125,
2127,
2133,
2163,
2173,
2187,
2209,
2211,
2215,
2217,
2221,
2239,
2251,
2253,
2257,
2271,
2277,
2281,
2283,
2301,
2311,
2317,
2323,
2335,
2343,
2355,
2365,
2379,
2395,
2403,
2407,
2409,
2415,
2419,
2427,
2439,
2445,
2461,
2467,
2473,
2479,
2491,
2493,
2505,
2511,
2523,
2527,
2545,
2557,
2563,
2571,
2575,
2587,
2589,
2593,
2599,
2607,
2625,
2635,
2647,
2649,
2653,
2661,
2667,
2671,
2689,
2697,
2715,
2725,
2755,
2763,
2773,
2781,
2785,
2787,
2797,
2815,
2817,
2821,
2823,
2827,
2835,
2841,
2845,
2851,
2877,
2887,
2899,
2901,
2905,
2913,
2923,
2943,
2953,
2961,
2971,
2973,
2977,
2983,
3003,
3007,
3027,
3031,
3037,
3039,
3049,
3055,
3073,
3075,
3091,
3097,
3099,
3109,
3111,
3121,
3123,
3133,
3153,
3163,
3171,
3175,
3183,
3187,
3199,
3213,
3223,
3229,
3235,
3243,
3259,
3261,
3289,
3297,
3301,
3307,
3313,
3325,
3339,
3351,
3355,
3363,
3381,
3403,
3405,
3409,
3411,
3427,
3433,
3439,
3451,
3453,
3465,
3477,
3481,
3487,
3489,
3495,
3499,
3507,
3559,
3565,
3571,
3579,
3595,
3597,
3603,
3607,
3613,
3621,
3625,
3633,
3655,
3661,
3663,
3669,
3675,
3685,
3687,
3697,
3709,
3717,
3721,
3727,
3747,
3753,
3763,
3771,
3781,
3789,
3793,
3795,
3811,
3843,
3847,
3849,
3865,
3873,
3879,
3889,
3891,
3897,
3909,
3915,
3931,
3943,
3951,
3955,
3969,
3975,
3981,
3991,
3999,
4003,
4015,
4023,
4033,
4035,
4041,
4045,
4063,
4069,
4081,
4095,
4105,
4107,
4129,
4131,
4161,
4165,
4173,
4179,
4189,
4195,
4201,
4203,
4207,
4227,
4237,
4251,
4255,
4257,
4263,
4269,
4285,
4287,
4315,
4321,
4329,
4335,
4363,
4377,
4383,
4389,
4399,
4413,
4431,
4441,
4443,
4455,
4461,
4465,
4483,
4485,
4495,
4509,
4519,
4521,
4539,
4551,
4561,
4567,
4569,
4573,
4587,
4609,
4611,
4621,
4623,
4629,
4645,
4647,
4653,
4663,
4671,
4675,
4695,
4699,
4713,
4717,
4725,
4741,
4761,
4767,
4773,
4797,
4801,
4809,
4813,
4819,
4833,
4837,
4839,
4843,
4851,
4863,
4867,
4881,
4887,
4893.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 609237 values, from 1 to 9999997).
n\r | 0 | 1 |
2 | 0 | 609237 | 2 |
3 | 305057 | 304180 | 0 | 3 |
4 | 0 | 304898 | 0 | 304339 | 4 |
5 | 121268 | 121583 | 122381 | 122907 | 121098 | 5 |
6 | 0 | 304180 | 0 | 305057 | 0 | 0 | 6 |
7 | 95430 | 95104 | 95241 | 114355 | 56710 | 57226 | 95171 | 7 |
8 | 0 | 152809 | 0 | 152093 | 0 | 152089 | 0 | 152246 | 8 |
9 | 95804 | 94972 | 0 | 95060 | 95098 | 0 | 114193 | 114110 | 0 | 9 |
10 | 0 | 121583 | 0 | 122907 | 0 | 121268 | 0 | 122381 | 0 | 121098 | 10 |
11 | 55684 | 55401 | 55416 | 55485 | 55468 | 55399 | 55125 | 55365 | 55050 | 55646 | 55198 |
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.