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Duffinian n.  and  super-d n.

First numbers that belong to both sets:

81, 119, 169, 219, 247, 319, 333, 335, 338, 381, 469, 471, 481, 511, 669, 715, 731, 749, 781, 784, 831, 869, 981, 1053, 1055, 1057, 1058, 1067, 1081, 1119, 1219, 1281, 1331, 1369, 1469, 1519, 1569, 1631, 1645, 1681, 1731, 1769, 1781, 1819, 1919, 1969, 1981, 2019, 2119, 2159, 2169, 2181, 2219, 2231, 2261, 2331, 2363, 2369, 2419, 2431, 2469, 2471, 2479, 2519, 2569, 2581, 2619, 2627, 2631, 2667, 2669, 2681, 2759, 2781, 2831, 2881, 2935, 2943, 2981, 3035, 3081, 3087, 3131, 3239, 3269, 3281, 3317, 3337, 3341, 3349, 3351, 3353, 3355, 3357, 3362, 3364, 3365, 3369, 3379, 3383, 3385, 3387, 3419, 3431, 3481, 3569, 3619, 3681, 3781, 3783, 3819, 3829, 3869, 3951, 3981, 4015, 4031, 4069, 4081, 4143, 4169, 4181, 4197, 4269, 4285, 4319, 4331, 4369, 4431, 4469, 4471, 4489, 4531, 4619, 4631, 4669, 4681, 4719, 4769, 4781, 4807, 4809, 4819, 4869, 4873, 4881, 4961, 4981, 5061, 5069, 5105, 5111, 5131, 5169, 5207, 5219, 5269, 5331, 5349, 5517, 5533, 5619, 5681, 5687, 5719, 5731, 5819, 5831, 5969, 6019, 6031, 6051, 6059, 6069, 6119, 6123, 6169, 6181, 6219, 6231, 6319, 6331, 6357, 6377, 6381, 6411, 6413, 6419, 6431, 6497, 6631, 6669, 6731, 6769, 6859, 6881, 6919, 6929, 6931, 6989, 7031, 7077, 7081, 7131, 7149, 7169, 7181, 7231, 7319, 7373, 7381, 7419, 7471, 7493, 7519, 7531, 7569, 7619, 7627, 7631, 7707, 7721, 7731, 7769, 7781, 7811, 7813, 7819, 7825, 7831, 7833, 7835, 7837, 7869, 7931, 7969, 7981, 8031, 8035, 8100, 8119, 8131, 8239, 8281, 8381, 8409, 8433, 8435, 8471, 8483, 8531, 8569, 8703, 8769, 8855, 8881, 8919, 8931, 8981, 9019, 9031, 9081, 9119, 9131, 9169, 9193, 9197, 9219, 9261, 9269, 9331, 9469, 9481, 9489, 9545, 9569, 9581, 9617, 9727, 9731.

Some larger examples :