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Duffinian n.  and  Ruth-Aaron pair

First numbers that belong to both sets:

8, 9, 16, 25, 49, 50, 77, 125, 493, 715, 949, 1331, 1682, 2107, 2491, 2601, 2783, 5405, 5561, 5959, 6557, 6867, 8281, 8464, 8855, 12727, 14587, 17081, 18491, 24433, 24881, 24895, 33019, 37829, 40081, 41261, 42625, 44831, 47545, 48203, 48763, 49241, 52555, 63665, 64233, 81175, 95709, 98119, 99163, 106799, 109939, 112079, 118657, 141341, 141489, 143623, 154843, 155111, 155709, 172773, 180359, 197657, 204259, 228599, 230125, 244036, 244595, 261019, 263327, 263629, 268657, 268715, 294335, 296111, 304325, 319429, 346693, 350599, 370349, 373703, 380963, 388451, 394855, 417163, 421819, 436933, 441211, 453475, 467303, 477093, 488977, 509851, 531991, 537917, 540281, 547525, 550033, 554683, 560151, 565823, 572015, 576985, 583463, 598249, 608317, 618751, 624079, 639847, 665323, 667629, 685229, 693611, 696437, 732089, 732199, 742853, 748231, 767833, 773605, 820601, 823151, 849375, 850747, 851709, 856607, 859409, 878899, 890723, 901747, 906019, 911075, 911537, 917863, 932035, 956039, 959581, 961573, 962141, 976375, 977281, 977779, 999073, 1006549, 1019425, 1023641, 1045951, 1053599, 1054829, 1062875, 1085875, 1104263, 1131811, 1172947, 1173149, 1173505, 1191133, 1191451, 1193983, 1199987, 1211899, 1232747, 1243501, 1246933, 1252097, 1261007, 1267919, 1293139, 1306247, 1330895, 1333025, 1354053, 1361071, 1386903, 1428857, 1474375, 1492031, 1496551, 1516787, 1550855, 1560499, 1562093, 1568683, 1570279, 1618789, 1672711, 1686751, 1686893, 1716629, 1744919, 1777027, 1797113, 1806367, 1806949, 1809709, 1818227, 1858645, 1864057, 1887185, 1915577, 1926235, 1945049, 1962797, 1967765, 2009351, 2020801, 2022343, 2024867, 2029949, 2042951, 2045977, 2048935, 2049319, 2065123, 2105237, 2120989, 2138929, 2179519, 2195567, 2260589, 2305397, 2314663, 2339047, 2390483, 2407321, 2442185, 2460437, 2559673, 2579309, 2586235, 2649041, 2660635, 2701657, 2701669, 2742395, 2781571, 2849043, 2854739, 2872493, 2892103, 2931775, 2947705, 2975951, 3002297, 3003469, 3009413, 3032761, 3062079, 3069207, 3155779, 3161665, 3164525, 3205915, 3206343, 3223789, 3240385, 3267441, 3352621, 3400891, 3402311, 3414889, 3423437, 3438521, 3468319, 3476965, 3481351, 3524497, 3561941, 3570731, 3573467, 3584053, 3602833, 3665135, 3668587, 3678809, 3696379, 3703589, 3743351, 3749429, 3772333, 3816037.

Some larger examples :