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gapful n.  and  modest n.

First numbers that belong to both sets:

1030, 1037, 1090, 1111, 1545, 1624, 1833, 1881, 2060, 2222, 2575, 2639, 3045, 3090, 3333, 4277, 4444, 4872, 5278, 5555, 6666, 7189, 7777, 8099, 8888, 9999, 10030, 10090, 10185, 10270, 10370, 11407, 12054, 12111, 15045, 15081, 15135, 15405, 15555, 18037, 18074, 19057, 19513, 20033, 20060, 20180, 20540, 20740, 20909, 22333, 24108, 24222, 25075, 25225, 25675, 25925, 26481, 26999, 27111, 28756, 30090, 30101, 30135, 30270, 30555, 30810, 32148, 35105, 35315, 35945, 36074, 36333, 38114, 40033, 40066, 40120, 40185, 40296, 40360, 42189, 44333, 44666, 45135, 45405, 48444, 49063, 50150, 50450, 53159, 54111, 55165, 55495, 57171, 60099, 60180, 60202, 60540, 64111, 65195, 65585, 66999, 70210, 70630, 75225, 75675, 80066, 80240, 80720, 85255, 85765, 88666, 90270, 90303, 90810, 95285, 95855, 96444, 100030, 100090, 100110, 100111, 100150, 100180, 100185, 100270, 100300, 100330, 100370, 100450, 100540, 100740, 100900, 100909, 100990, 101010, 102999, 103030, 104148, 105135, 105315, 105405, 105555, 105945, 108444, 108972, 109090, 109327, 110121, 110270, 110330, 110370, 110990, 111111, 112333, 112336, 112504, 112518, 115185, 115621, 119357, 120099, 120132, 120135, 120180, 120270, 120360, 120370, 120405, 120540, 120555, 120740, 120810, 120888, 121212, 121999, 124279, 125333, 125454, 125925, 126243, 126378, 128576, 128592, 129387, 130143, 130185, 130270, 130370, 130390, 131313, 132594, 132891, 133399, 135405, 135555, 136444, 136629, 138333, 139417, 140148, 140154, 140180, 140210, 140270, 140370, 140420, 140540, 140630, 140740, 140777, 140999, 141414, 144432, 144648, 144972, 145185, 149447, 150033, 150045, 150135, 150165, 150225, 150270, 150297, 150370, 150405, 150450, 150495, 150555, 150675, 150810, 151333, 151485, 151515, 152684, 154231, 154545, 156324, 159477, 159999, 160176, 160180, 160185, 160240, 160270, 160303, 160360, 160370, 160480, 160540, 160720, 160740, 161616, 164333, 164369, 164444, 165405, 165495, 165555, 165891, 168252, 168504, 169507, 170187, 170270, 170370, 170510, 171717, 172774, 175185, 176592, 177333, 178999, 179537, 180054, 180081, 180198, 180270, 180370, 180405.

Some larger examples :