A number that divided by the sum of its digits gives a prime number. more
The first 600 Moran numbers :
18,
21,
27,
42,
45,
63,
84,
111,
114,
117,
133,
152,
153,
156,
171,
190,
195,
198,
201,
207,
209,
222,
228,
247,
261,
266,
285,
333,
370,
372,
399,
402,
407,
423,
444,
465,
481,
511,
516,
518,
531,
555,
558,
592,
603,
629,
645,
666,
711,
730,
732,
738,
774,
777,
801,
803,
804,
846,
888,
915,
954,
999,
1011,
1016,
1017,
1090,
1095,
1098,
1101,
1141,
1143,
1164,
1168,
1185,
1233,
1236,
1251,
1270,
1278,
1304,
1308,
1341,
1387,
1413,
1417,
1455,
1494,
1503,
1524,
1526,
1545,
1611,
1630,
1635,
1651,
1659,
1679,
1744,
1746,
1810,
1812,
1818,
1853,
1854,
1896,
1898,
1905,
1926,
1962,
2007,
2022,
2043,
2061,
2085,
2119,
2151,
2159,
2172,
2202,
2265,
2282,
2286,
2289,
2313,
2316,
2353,
2355,
2358,
2398,
2421,
2445,
2466,
2532,
2534,
2608,
2667,
2682,
2710,
2715,
2718,
2771,
2794,
2826,
2889,
2919,
2934,
3031,
3032,
3033,
3070,
3077,
3097,
3123,
3141,
3165,
3184,
3231,
3252,
3258,
3297,
3303,
3324,
3345,
3383,
3411,
3435,
3438,
3439,
3474,
3501,
3523,
3546,
3582,
3586,
3615,
3699,
3749,
3768,
3781,
3980,
3982,
4041,
4044,
4065,
4086,
4113,
4155,
4179,
4194,
4203,
4245,
4311,
4330,
4336,
4338,
4378,
4404,
4518,
4577,
4605,
4607,
4626,
4683,
4734,
4776,
4809,
4842,
4887,
4912,
4975,
5013,
5052,
5055,
5058,
5094,
5121,
5149,
5161,
5219,
5230,
5235,
5274,
5306,
5410,
5496,
5505,
5526,
5634,
5691,
5697,
5706,
5784,
5817,
5833,
5943,
5962,
6062,
6064,
6066,
6130,
6135,
6246,
6282,
6310,
6315,
6331,
6352,
6354,
6443,
6447,
6462,
6573,
6606,
6648,
6714,
6754,
6775,
6777,
6792,
6822,
6939,
6951,
7033,
7077,
7146,
7212,
7218,
7305,
7322,
7329,
7361,
7362,
7368,
7479,
7501,
7542,
7543,
7580,
7587,
7588,
7675,
7707,
7833,
7859,
7902,
7940,
7944,
7982,
8082,
8088,
8110,
8115,
8203,
8205,
8226,
8227,
8289,
8334,
8337,
8338,
8376,
8397,
8406,
8559,
8596,
8622,
8660,
8717,
8734,
8808,
8841,
8937,
8952,
9012,
9015,
9054,
9093,
9096,
9099,
9105,
9162,
9219,
9232,
9253,
9369,
9414,
9475,
9526,
9528,
9693,
9723,
9740,
9816,
9854,
9909,
9925,
10012,
10014,
10053,
10090,
10095,
10096,
10107,
10109,
10161,
10213,
10232,
10236,
10278,
10279,
10307,
10308,
10346,
10365,
10386,
10479,
10524,
10543,
10566,
10630,
10635,
10674,
10727,
10782,
10818,
10901,
10905,
10926,
10963,
10968,
10983,
11007,
11028,
11061,
11085,
11133,
11170,
11202,
11241,
11244,
11265,
11331,
11354,
11355,
11358,
11487,
11511,
11530,
11535,
11538,
11574,
11601,
11604,
11606,
11646,
11647,
11688,
11710,
11754,
11805,
11824,
11862,
11976,
11991,
12102,
12108,
12165,
12181,
12186,
12252,
12294,
12303,
12345,
12362,
12435,
12438,
12563,
12612,
12618,
12694,
12747,
12762,
12873,
12942,
12984,
13023,
13044,
13086,
13111,
13116,
13117,
13118,
13131,
13155,
13194,
13245,
13264,
13374,
13401,
13404,
13486,
13518,
13598,
13605,
13626,
13842,
13848,
13881,
13882,
13914,
14031,
14052,
14055,
14093,
14099,
14103,
14126,
14128,
14166,
14211,
14230,
14346,
14383,
14412,
14505,
14521,
14562,
14568,
14704,
14769,
14780,
14814,
14856,
14922,
15001,
15003,
15021,
15135,
15223,
15267,
15310,
15315,
15354,
15393,
15409,
15426,
15462,
15519,
15534,
15579,
15623,
15689,
15751,
15771,
15775,
15849,
15864,
15938,
16035,
16101,
16142,
16144,
16149,
16210,
16258,
16305,
16326,
16389,
16527,
16542,
16580,
16584,
16654,
16659,
16722,
17001,
17008,
17046,
17153,
17154,
17283,
17406,
17409,
17448,
17461,
17469,
17592,
17660,
17668,
17736,
17777,
17793,
17803,
17842,
17847,
17887,
17913,
18010,
18015,
18039,
18071,
18162,
18168,
18234,
18238,
18279,
18299,
18342,
18380,
18417,
18456,
18475,
18543,
18653,
18657,
18702,
18740,
18925,
18927,
19047,
19067,
19134,
19171,
19242,
19426,
19464,
19601,
19629,
19682,
19752,
19791,
19820,
19953,
20024,
20028,
20133,
20137,
20151,
20170,
20197,
20312,
20316,
20371,
20403,
20421,
20426,
20464,
20530,
20603,
20715,
20718,
20752,
20754,
20934,
20937,
21036,
21051,
21073,
21078,
21102.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 642344 values, from 18 to 99999965).
n\r | 0 | 1 |
2 | 327879 | 314465 | 2 |
3 | 430067 | 102147 | 110130 | 3 |
4 | 175995 | 159091 | 151884 | 155374 | 4 |
5 | 138022 | 136059 | 124212 | 128641 | 115410 | 5 |
6 | 222334 | 52506 | 55904 | 207733 | 49641 | 54226 | 6 |
7 | 75719 | 94216 | 94322 | 94721 | 94409 | 94816 | 94141 | 7 |
8 | 56452 | 80472 | 75765 | 78538 | 119543 | 78619 | 76119 | 76836 | 8 |
9 | 212296 | 35536 | 39953 | 118485 | 32432 | 33121 | 99286 | 34179 | 37056 | 9 |
10 | 70306 | 74030 | 68788 | 67035 | 65150 | 67716 | 62029 | 55424 | 61606 | 50260 | 10 |
11 | 55273 | 58857 | 58608 | 59073 | 58256 | 59347 | 57800 | 59203 | 57896 | 59252 | 58779 |
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.