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 |
2 | 4888863 | 4888863 | 2 |
3 | 3259242 | 3259242 | 3259242 | 3 |
4 | 2444433 | 2444430 | 2444430 | 2444433 | 4 |
5 | 1955545 | 1955545 | 1955545 | 1955546 | 1955545 | 5 |
6 | 1629621 | 1629607 | 1629607 | 1629621 | 1629635 | 1629635 | 6 |
7 | 1396826 | 1396813 | 1396813 | 1396826 | 1396813 | 1396822 | 1396813 | 7 |
8 | 1222217 | 1222214 | 1222216 | 1222216 | 1222216 | 1222216 | 1222214 | 1222217 | 8 |
9 | 1086414 | 1086414 | 1086414 | 1086414 | 1086414 | 1086414 | 1086414 | 1086414 | 1086414 | 9 |
10 | 977773 | 977773 | 977773 | 977773 | 977772 | 977772 | 977772 | 977772 | 977773 | 977773 | 10 |
11 | 889064 | 887966 | 889064 | 889066 | 889064 | 887966 | 889064 | 889176 | 889060 | 889060 | 889176 |
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.