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junction numbers
A number that can be written as x + sod(x) for at least two x. more

The first 600 junction numbers :
101, 103, 105, 107, 109, 111, 113, 115, 117, 202, 204, 206, 208, 210, 212, 214, 216, 218, 303, 305, 307, 309, 311, 313, 315, 317, 319, 404, 406, 408, 410, 412, 414, 416, 418, 420, 505, 507, 509, 511, 513, 515, 517, 519, 521, 606, 608, 610, 612, 614, 616, 618, 620, 622, 707, 709, 711, 713, 715, 717, 719, 721, 723, 808, 810, 812, 814, 816, 818, 820, 822, 824, 909, 911, 913, 915, 917, 919, 921, 923, 925, 1001, 1003, 1005, 1007, 1009, 1011, 1012, 1013, 1014, 1015, 1016, 1018, 1020, 1022, 1024, 1026, 1102, 1104, 1106, 1108, 1110, 1112, 1114, 1116, 1118, 1203, 1205, 1207, 1209, 1211, 1213, 1215, 1217, 1219, 1304, 1306, 1308, 1310, 1312, 1314, 1316, 1318, 1320, 1405, 1407, 1409, 1411, 1413, 1415, 1417, 1419, 1421, 1506, 1508, 1510, 1512, 1514, 1516, 1518, 1520, 1522, 1607, 1609, 1611, 1613, 1615, 1617, 1619, 1621, 1623, 1708, 1710, 1712, 1714, 1716, 1718, 1720, 1722, 1724, 1809, 1811, 1813, 1815, 1817, 1819, 1821, 1823, 1825, 1910, 1912, 1914, 1916, 1918, 1920, 1922, 1924, 1926, 2002, 2004, 2006, 2008, 2010, 2012, 2013, 2014, 2015, 2016, 2017, 2019, 2021, 2023, 2025, 2027, 2103, 2105, 2107, 2109, 2111, 2113, 2115, 2117, 2119, 2204, 2206, 2208, 2210, 2212, 2214, 2216, 2218, 2220, 2305, 2307, 2309, 2311, 2313, 2315, 2317, 2319, 2321, 2406, 2408, 2410, 2412, 2414, 2416, 2418, 2420, 2422, 2507, 2509, 2511, 2513, 2515, 2517, 2519, 2521, 2523, 2608, 2610, 2612, 2614, 2616, 2618, 2620, 2622, 2624, 2709, 2711, 2713, 2715, 2717, 2719, 2721, 2723, 2725, 2810, 2812, 2814, 2816, 2818, 2820, 2822, 2824, 2826, 2911, 2913, 2915, 2917, 2919, 2921, 2923, 2925, 2927, 3003, 3005, 3007, 3009, 3011, 3013, 3014, 3015, 3016, 3017, 3018, 3020, 3022, 3024, 3026, 3028, 3104, 3106, 3108, 3110, 3112, 3114, 3116, 3118, 3120, 3205, 3207, 3209, 3211, 3213, 3215, 3217, 3219, 3221, 3306, 3308, 3310, 3312, 3314, 3316, 3318, 3320, 3322, 3407, 3409, 3411, 3413, 3415, 3417, 3419, 3421, 3423, 3508, 3510, 3512, 3514, 3516, 3518, 3520, 3522, 3524, 3609, 3611, 3613, 3615, 3617, 3619, 3621, 3623, 3625, 3710, 3712, 3714, 3716, 3718, 3720, 3722, 3724, 3726, 3811, 3813, 3815, 3817, 3819, 3821, 3823, 3825, 3827, 3912, 3914, 3916, 3918, 3920, 3922, 3924, 3926, 3928, 4004, 4006, 4008, 4010, 4012, 4014, 4015, 4016, 4017, 4018, 4019, 4021, 4023, 4025, 4027, 4029, 4105, 4107, 4109, 4111, 4113, 4115, 4117, 4119, 4121, 4206, 4208, 4210, 4212, 4214, 4216, 4218, 4220, 4222, 4307, 4309, 4311, 4313, 4315, 4317, 4319, 4321, 4323, 4408, 4410, 4412, 4414, 4416, 4418, 4420, 4422, 4424, 4509, 4511, 4513, 4515, 4517, 4519, 4521, 4523, 4525, 4610, 4612, 4614, 4616, 4618, 4620, 4622, 4624, 4626, 4711, 4713, 4715, 4717, 4719, 4721, 4723, 4725, 4727, 4812, 4814, 4816, 4818, 4820, 4822, 4824, 4826, 4828, 4913, 4915, 4917, 4919, 4921, 4923, 4925, 4927, 4929, 5005, 5007, 5009, 5011, 5013, 5015, 5016, 5017, 5018, 5019, 5020, 5022, 5024, 5026, 5028, 5030, 5106, 5108, 5110, 5112, 5114, 5116, 5118, 5120, 5122, 5207, 5209, 5211, 5213, 5215, 5217, 5219, 5221, 5223, 5308, 5310, 5312, 5314, 5316, 5318, 5320, 5322, 5324, 5409, 5411, 5413, 5415, 5417, 5419, 5421, 5423, 5425, 5510, 5512, 5514, 5516, 5518, 5520, 5522, 5524, 5526, 5611, 5613, 5615, 5617, 5619, 5621, 5623, 5625, 5627, 5712, 5714, 5716, 5718, 5720, 5722, 5724, 5726, 5728, 5813, 5815, 5817, 5819, 5821, 5823, 5825, 5827, 5829, 5914, 5916, 5918, 5920, 5922, 5924, 5926, 5928, 5930, 6006, 6008, 6010, 6012, 6014, 6016, 6017, 6018, 6019, 6020, 6021, 6023, 6025, 6027, 6029, 6031, 6107, 6109, 6111, 6113, 6115, 6117, 6119, 6121, 6123, 6208, 6210, 6212, 6214, 6216, 6218, 6220, 6222, 6224.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 9777726 values, from 101 to 99999970).

n\r 0  1 
248888634888863 2 
3325924232592423259242 3 
42444433244443024444302444433 4 
519555451955545195554519555461955545 5 
6162962116296071629607162962116296351629635 6 
71396826139681313968131396826139681313968221396813 7 
812222171222214122221612222161222216122221612222141222217 8 
9108641410864141086414108641410864141086414108641410864141086414 9 
10977773977773977773977773977772977772977772977772977773977773 10 
11889064887966889064889066889064887966889064889176889060889060889176

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.