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Duffinian n.  and  self n.

First numbers that belong to both sets:

9, 64, 75, 121, 143, 187, 209, 299, 323, 400, 413, 512, 525, 749, 793, 815, 817, 905, 1043, 1111, 1133, 1177, 1313, 1357, 1379, 1469, 1513, 1537, 1603, 1649, 1682, 1739, 1805, 1829, 1919, 1963, 1985, 2007, 2033, 2077, 2123, 2189, 2257, 2279, 2312, 2369, 2413, 2527, 2615, 2705, 2773, 2795, 2817, 2863, 2885, 2975, 2997, 3113, 3179, 3225, 3247, 3269, 3337, 3403, 3427, 3493, 3605, 3629, 3763, 3785, 3875, 3897, 3965, 4009, 4147, 4169, 4213, 4237, 4303, 4393, 4415, 4417, 4439, 4505, 4529, 4573, 4617, 4619, 4685, 4707, 4775, 4819, 4843, 4887, 4955, 4977, 5025, 5047, 5069, 5137, 5159, 5249, 5293, 5315, 5317, 5339, 5405, 5429, 5473, 5495, 5517, 5585, 5618, 5675, 5697, 5719, 5765, 5776, 5787, 5809, 5833, 5855, 5899, 5921, 5989, 6059, 6103, 6127, 6193, 6215, 6239, 6272, 6283, 6305, 6419, 6463, 6485, 6507, 6575, 6597, 6665, 6755, 6799, 6821, 6845, 6867, 6889, 6979, 7049, 7093, 7115, 7117, 7139, 7183, 7273, 7317, 7319, 7363, 7385, 7396, 7407, 7442, 7453, 7475, 7519, 7543, 7609, 7633, 7655, 7677, 7688, 7721, 7811, 7835, 7857, 7923, 7925, 7947, 7969, 7991, 8013, 8083, 8105, 8129, 8173, 8285, 8375, 8465, 8509, 8533, 8621, 8711, 8735, 8801, 8825, 8836, 8891, 8913, 8937, 8959, 8981, 9003, 9073, 9095, 9119, 9163, 9185, 9253, 9275, 9297, 9365, 9409, 9477, 9499, 9523, 9545, 9567, 9589, 9611, 9635, 9701, 9723, 9813, 9837, 9881, 9903, 9925, 9971, 9993, 10043, 10109, 10199, 10379, 10447, 10469, 10537, 10603, 10649, 10693, 10715, 10717, 10783, 10805, 10816, 10873, 10917, 10919, 10952, 10963, 11033, 11077, 11099, 11123, 11167, 11189, 11325, 11347, 11413, 11615, 11639, 11683, 11705, 11729, 11773, 11795, 11819, 11885, 11997, 12023, 12067, 12089, 12100, 12179, 12225, 12247, 12313, 12337, 12359, 12427, 12449.

Some larger examples :