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Ruth-Aaron pair  and  self n.

First numbers that belong to both sets:

5, 9, 154, 714, 1682, 1862, 2492, 2784, 4191, 5405, 6867, 13775, 37882, 43216, 44891, 52554, 57076, 64232, 89979, 106800, 109939, 112079, 141340, 143623, 183447, 224105, 268192, 333802, 350599, 361063, 381728, 394855, 416119, 457899, 470119, 477093, 583462, 587264, 671019, 685228, 694430, 732199, 740727, 748230, 788671, 820601, 838935, 839376, 869054, 890127, 901748, 906020, 911075, 932034, 956040, 959581, 965095, 977895, 1045950, 1085875, 1166067, 1191133, 1211899, 1232746, 1243500, 1252096, 1275731, 1302092, 1330407, 1496780, 1549454, 1570279, 1575262, 1607045, 1686893, 1711142, 1716628, 1754463, 1762124, 1777027, 1809710, 1818227, 1921424, 2003631, 2055087, 2065123, 2094808, 2120989, 2123667, 2179520, 2236336, 2387376, 2390482, 2437225, 2460436, 2493800, 2649041, 2701669, 2778560, 2834766, 2849043, 2923921, 2931775, 2975952, 2992220, 3009412, 3056976, 3198041, 3205915, 3267442, 3423436, 3468320, 3570731, 3584196, 3696380, 3743351, 3771429, 3978260, 4010181, 4010552, 4076327, 4086227, 4091403, 4141524, 4142839, 4376152, 4462339, 4596863, 4599877, 4614731, 4799012, 4826835, 4832665, 4874221, 4954053, 4958988, 5096736, 5185520, 5219138, 5240014, 5313436, 5346229, 5469918, 5535655, 5733846, 5854086, 5932509, 6126439, 6209665, 6226910, 6245799, 6307910, 6384994, 6540898, 6607509, 6608128, 6811833, 6860275, 6963437, 7084296, 7293254, 7295625, 7331651, 7376941, 7403008, 7580444, 7681681, 7690288, 8190576, 8256680, 8471040, 8505407, 8534835, 8596070, 8596608, 8630496, 8735188, 8746897, 8800732, 8818146, 8967013, 9178976, 9200861, 9210728, 9249751, 9532061, 9819069, 10269216, 10642459, 10810625, 10876547, 10902188, 11032295, 11249575, 11498401, 11612929, 11690731, 11818577, 12013576, 12245280, 12282920, 12478016, 12737791, 12830741, 13215750, 13323425, 13335988, 13371641, 13552451, 13619444, 13701480, 14138362, 14408990, 14587695, 14618600, 14650899, 14693368, 14752342, 14790232, 14833476, 15004421, 15196760, 15380575, 15455196, 15546096, 15684896, 15775616, 15784482, 15898036, 16052427, 16117326, 16171934, 16216607, 16400053, 16401829, 16417430, 16578315, 16602112, 16637952, 16678518, 16746301, 16816334, 16839394, 16927897, 16995252, 17247153, 17297753, 17499700, 17508568, 17518725, 17999683, 18071766, 18169864, 18175176, 18185300, 18216341, 18316509, 18392177, 18396585, 18424039, 18563548, 19117318, 19173355, 19357954, 19469352, 19495250, 19727808, 19784811, 19871202, 19905145, 19911085, 19968209, 19987344, 20148125, 20642280, 20733035, 20761776, 21256978, 21271661, 21325088.

Some larger examples :