A number which cannot be written as x + sod(x). more
The first 600 self or Colombian numbers :
1,
3,
5,
7,
9,
20,
31,
42,
53,
64,
75,
86,
97,
108,
110,
121,
132,
143,
154,
165,
176,
187,
198,
209,
211,
222,
233,
244,
255,
266,
277,
288,
299,
310,
312,
323,
334,
345,
356,
367,
378,
389,
400,
411,
413,
424,
435,
446,
457,
468,
479,
490,
501,
512,
514,
525,
536,
547,
558,
569,
580,
591,
602,
613,
615,
626,
637,
648,
659,
670,
681,
692,
703,
714,
716,
727,
738,
749,
760,
771,
782,
793,
804,
815,
817,
828,
839,
850,
861,
872,
883,
894,
905,
916,
918,
929,
940,
951,
962,
973,
984,
995,
1006,
1021,
1032,
1043,
1054,
1065,
1076,
1087,
1098,
1109,
1111,
1122,
1133,
1144,
1155,
1166,
1177,
1188,
1199,
1210,
1212,
1223,
1234,
1245,
1256,
1267,
1278,
1289,
1300,
1311,
1313,
1324,
1335,
1346,
1357,
1368,
1379,
1390,
1401,
1412,
1414,
1425,
1436,
1447,
1458,
1469,
1480,
1491,
1502,
1513,
1515,
1526,
1537,
1548,
1559,
1570,
1581,
1592,
1603,
1614,
1616,
1627,
1638,
1649,
1660,
1671,
1682,
1693,
1704,
1715,
1717,
1728,
1739,
1750,
1761,
1772,
1783,
1794,
1805,
1816,
1818,
1829,
1840,
1851,
1862,
1873,
1884,
1895,
1906,
1917,
1919,
1930,
1941,
1952,
1963,
1974,
1985,
1996,
2007,
2022,
2033,
2044,
2055,
2066,
2077,
2088,
2099,
2110,
2112,
2123,
2134,
2145,
2156,
2167,
2178,
2189,
2200,
2211,
2213,
2224,
2235,
2246,
2257,
2268,
2279,
2290,
2301,
2312,
2314,
2325,
2336,
2347,
2358,
2369,
2380,
2391,
2402,
2413,
2415,
2426,
2437,
2448,
2459,
2470,
2481,
2492,
2503,
2514,
2516,
2527,
2538,
2549,
2560,
2571,
2582,
2593,
2604,
2615,
2617,
2628,
2639,
2650,
2661,
2672,
2683,
2694,
2705,
2716,
2718,
2729,
2740,
2751,
2762,
2773,
2784,
2795,
2806,
2817,
2819,
2830,
2841,
2852,
2863,
2874,
2885,
2896,
2907,
2918,
2920,
2931,
2942,
2953,
2964,
2975,
2986,
2997,
3008,
3023,
3034,
3045,
3056,
3067,
3078,
3089,
3100,
3111,
3113,
3124,
3135,
3146,
3157,
3168,
3179,
3190,
3201,
3212,
3214,
3225,
3236,
3247,
3258,
3269,
3280,
3291,
3302,
3313,
3315,
3326,
3337,
3348,
3359,
3370,
3381,
3392,
3403,
3414,
3416,
3427,
3438,
3449,
3460,
3471,
3482,
3493,
3504,
3515,
3517,
3528,
3539,
3550,
3561,
3572,
3583,
3594,
3605,
3616,
3618,
3629,
3640,
3651,
3662,
3673,
3684,
3695,
3706,
3717,
3719,
3730,
3741,
3752,
3763,
3774,
3785,
3796,
3807,
3818,
3820,
3831,
3842,
3853,
3864,
3875,
3886,
3897,
3908,
3919,
3921,
3932,
3943,
3954,
3965,
3976,
3987,
3998,
4009,
4024,
4035,
4046,
4057,
4068,
4079,
4090,
4101,
4112,
4114,
4125,
4136,
4147,
4158,
4169,
4180,
4191,
4202,
4213,
4215,
4226,
4237,
4248,
4259,
4270,
4281,
4292,
4303,
4314,
4316,
4327,
4338,
4349,
4360,
4371,
4382,
4393,
4404,
4415,
4417,
4428,
4439,
4450,
4461,
4472,
4483,
4494,
4505,
4516,
4518,
4529,
4540,
4551,
4562,
4573,
4584,
4595,
4606,
4617,
4619,
4630,
4641,
4652,
4663,
4674,
4685,
4696,
4707,
4718,
4720,
4731,
4742,
4753,
4764,
4775,
4786,
4797,
4808,
4819,
4821,
4832,
4843,
4854,
4865,
4876,
4887,
4898,
4909,
4920,
4922,
4933,
4944,
4955,
4966,
4977,
4988,
4999,
5010,
5025,
5036,
5047,
5058,
5069,
5080,
5091,
5102,
5113,
5115,
5126,
5137,
5148,
5159,
5170,
5181,
5192,
5203,
5214,
5216,
5227,
5238,
5249,
5260,
5271,
5282,
5293,
5304,
5315,
5317,
5328,
5339,
5350,
5361,
5372,
5383,
5394,
5405,
5416,
5418,
5429,
5440,
5451,
5462,
5473,
5484,
5495,
5506,
5517,
5519,
5530,
5541,
5552,
5563,
5574,
5585,
5596,
5607,
5618,
5620,
5631,
5642,
5653,
5664,
5675,
5686,
5697,
5708,
5719,
5721,
5732,
5743,
5754,
5765,
5776,
5787,
5798,
5809,
5820,
5822,
5833,
5844,
5855,
5866,
5877,
5888,
5899,
5910,
5921,
5923,
5934,
5945,
5956,
5967,
5978,
5989,
6000,
6011,
6026,
6037,
6048,
6059,
6070,
6081,
6092.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 9778655 values, from 1 to 100000076).
n\r | 0 | 1 |
2 | 4889326 | 4889329 | 2 |
3 | 3259551 | 3259551 | 3259553 | 3 |
4 | 2444666 | 2444663 | 2444660 | 2444666 | 4 |
5 | 1955731 | 1955733 | 1955730 | 1955732 | 1955729 | 5 |
6 | 1629775 | 1629751 | 1629751 | 1629776 | 1629800 | 1629802 | 6 |
7 | 1396952 | 1396950 | 1396952 | 1396952 | 1396939 | 1396970 | 1396940 | 7 |
8 | 1222337 | 1222334 | 1222328 | 1222330 | 1222329 | 1222329 | 1222332 | 1222336 | 8 |
9 | 1086517 | 1086516 | 1086519 | 1086517 | 1086518 | 1086518 | 1086517 | 1086517 | 1086516 | 9 |
10 | 977866 | 977868 | 977866 | 977867 | 977864 | 977865 | 977865 | 977864 | 977865 | 977865 | 10 |
11 | 890063 | 888962 | 890056 | 880059 | 890056 | 888959 | 890056 | 890170 | 890045 | 890063 | 890166 |
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.