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self or Colombian numbers
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 
248893264889329 2 
3325955132595513259553 3 
42444666244466324446602444666 4 
519557311955733195573019557321955729 5 
6162977516297511629751162977616298001629802 6 
71396952139695013969521396952139693913969701396940 7 
812223371222334122232812223301222329122232912223321222336 8 
9108651710865161086519108651710865181086518108651710865171086516 9 
10977866977868977866977867977864977865977865977864977865977865 10 
11890063888962890056880059890056888959890056890170890045890063890166

A pictorial representation of the table above
motab
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.