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lucky n.  and  modest n.

First numbers that belong to both sets:

13, 49, 69, 79, 111, 133, 211, 327, 399, 409, 433, 511, 699, 777, 927, 933, 981, 1009, 1011, 1233, 1339, 1533, 1545, 1599, 1827, 1833, 1899, 1933, 2127, 2133, 2163, 2427, 2545, 2575, 2599, 2781, 2877, 2899, 3027, 3037, 3055, 3099, 3111, 3133, 3199, 3451, 3499, 3999, 4045, 4263, 4399, 4699, 4963, 4977, 4999, 5299, 5599, 6009, 6111, 6399, 6999, 7009, 7077, 7111, 7299, 7333, 7899, 8037, 8299, 9081, 9399, 9999, 10003, 10009, 10111, 10555, 10909, 11407, 12333, 12999, 13027, 13117, 14037, 15081, 15333, 16333, 18333, 19333, 20101, 20185, 21027, 21111, 21189, 21567, 22099, 22333, 22999, 23037, 23851, 24037, 24333, 25185, 25225, 27037, 27333, 30303, 30999, 31093, 32727, 33297, 33333, 36037, 39481, 40101, 40333, 40555, 40999, 42063, 42189, 42567, 43129, 43333, 45081, 45111, 45555, 46069, 46999, 48081, 48999, 49111, 49147, 50101, 51459, 54729, 55555, 57081, 57111, 57333, 58087, 58261, 58999, 60555, 60909, 61183, 61999, 63111, 63243, 63777, 64333, 65481, 66297, 67333, 69333, 69999, 70063, 70077, 70105, 70333, 70707, 70945, 72243, 72333, 75111, 75675, 75925, 77407, 80185, 81111, 82111, 82123, 84189, 84999, 85255, 85333, 85555, 85999, 87111, 87261, 87783, 88333, 90099, 90891, 91111, 91333, 92727, 92851, 94423, 95185, 96333, 97999, 99333, 100123, 100333, 100813, 101515, 102153, 102439, 102459, 103309, 103333, 105135, 105189, 105259, 105405, 105777, 108111, 108243, 108333, 108999, 109327, 111111, 111999, 112189, 114999, 115135, 115185, 117481, 120405, 120555, 120909, 121407, 123999, 124333, 125185, 126189, 126243, 126567, 126777, 127333, 129999, 130033, 130143, 130195, 130333, 130351, 131313, 132891, 132999, 133939, 136333, 136629, 136999, 138207, 138333, 138999, 140185, 142333, 150045, 150055, 150297, 150333, 151333, 151453, 151999, 153333, 154297, 154545, 156333, 156351, 159333, 159999, 160033, 160999, 161259, 166333, 166999, 168259, 168777, 171111, 171333, 171717, 171999, 174333, 174999, 175185, 175225, 175315, 175333, 175777, 175945.

Some larger examples :