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junction n.  and  Ruth-Aaron pair

First numbers that belong to both sets:

105, 715, 1520, 2107, 12726, 16932, 24025, 33019, 33020, 37828, 42624, 43215, 44832, 63427, 79119, 98120, 110608, 132210, 143622, 148215, 155112, 244035, 261019, 261020, 263328, 263629, 304326, 319429, 381729, 407835, 416120, 421819, 436932, 441211, 461825, 470120, 501830, 525224, 547525, 550032, 550033, 557536, 564924, 565824, 572016, 608317, 665322, 667629, 671020, 685229, 694431, 696437, 740726, 748231, 767832, 838936, 842127, 882927, 890126, 890724, 906019, 909624, 932035, 942633, 956039, 1003513, 1019425, 1054828, 1246932, 1275730, 1329130, 1333025, 1386537, 1431213, 1492031, 1609737, 1671334, 1716629, 1762125, 1773135, 1777026, 1799941, 1818228, 1858644, 1921425, 1926236, 2048935, 2049318, 2065122, 2138929, 2407320, 2437224, 2527020, 2538533, 2586235, 2649042, 2660634, 2849042, 2854740, 3026019, 3094039, 3164525, 3198042, 3268126, 3291130, 3352621, 3402312, 3561940, 3570732, 3602833, 3629031, 3629032, 3632535, 3665135, 3749429, 3771430, 3772332, 3816037, 3835132, 3865731, 3889343, 3950120, 4057123, 4076328, 4086226, 4141523, 4160530, 4389539, 4416040, 4614730, 4763626, 4826836, 4913219, 4970224, 5096735, 5140317, 5240013, 5241035, 5242032, 5267844, 5346228, 5434626, 5560232, 6029536, 6161832, 6242131, 6262319, 6313724, 6447536, 6496328, 6521031, 6549846, 6608127, 6649050, 6668947, 6689332, 6803928, 6811834, 6963438, 6981341, 6999643, 7094933, 7096527, 7120224, 7145032, 7191735, 7267028, 7271120, 7304432, 7376940, 7396532, 7587447, 7718336, 7874051, 7985237, 8008131, 8062119, 8471039, 8476439, 8534834, 8800733, 8976852, 9018426, 9086046, 9210729, 9251928, 9263525, 9366030, 9512837, 9576229, 9697639, 9780238, 9790429, 9825127, 9981936, 10261719, 10727936, 10774225, 10810624, 10812824, 10974128, 11143935, 11305430, 11322922, 11341214, 11386528, 11587931, 11595324, 11612930, 11625839, 11690730, 11814940, 11857337, 11930048, 12013617, 12173319, 12189629, 12369044, 12563425, 12573931, 12697035, 12697036, 12817637, 12910821, 13160027, 13160028, 13237024, 13323424, 13593631, 13896532, 13902835, 13909543, 13979736, 14478543, 14510320, 14606425, 14646835, 14742739, 14746236, 14747544, 14790233, 15004420, 15021930, 15174325, 15411533, 15587127, 15824931, 15898037, 16051231, 16052428, 16117325, 16171935, 16233318, 16247830, 16335436, 16400054, 16401828, 16417431, 16725128, 16771045, 16816335, 17058427, 17727836, 17905731, 18151119, 18172439, 18424040, 18507033, 18507034, 18958249, 19184040, 19312224, 19662949, 19907442, 19936244, 19987345, 20148124, 20178636, 20444723, 20562827.

Some larger examples :