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gapful n.  and  repunit

First numbers that belong to both sets:

121, 341, 400, 781, 1111, 1365, 2380, 4095, 6175, 12720, 12883, 16003, 17823, 20440, 25260, 32581, 43473, 49063, 103363, 106080, 107913, 111111, 116623, 120100, 139503, 149383, 151740, 154843, 165243, 168421, 169456, 178809, 188500, 192283, 208920, 249501, 254080, 265720, 270921, 280371, 353431, 363007, 377611, 391251, 407683, 424453, 464443, 499360, 607621, 969241, 1047553, 1048575, 1074333, 1088893, 1103440, 1116193, 1135785, 1184833, 1213303, 1228773, 1236600, 1257763, 1307020, 1330563, 1360723, 1377103, 1380064, 1407783, 1455780, 1484743, 1508598, 1516593, 1533883, 1566253, 1615420, 1647373, 1680913, 1699113, 1699440, 1733173, 1742521, 1818453, 1830855, 1853683, 1872793, 1876120, 1908543, 1926221, 1997983, 2064640, 2086581, 2147691, 2163460, 2174151, 2236521, 2265384, 2317525, 2370460, 2400951, 2466471, 2478736, 2494821, 2561601, 2590260, 2613660, 2705080, 2737371, 2807301, 2837541, 2908731, 2944800, 3249007, 3330300, 3365391, 3439171, 3480091, 3555111, 3600507, 3950157, 3958111, 4045120, 4357480, 4466883, 4594593, 4650493, 4685520, 4780783, 5164257, 5232657, 5482929, 6322711, 6633201, 6809491, 6982807, 7004544, 8912800, 9009003, 9042385, 9117381, 9256807, 9262893, 9514141, 9675211, 9837633, 10039393, 10121943, 10166533, 10249603, 10265620, 10407975, 10455523, 10539763, 10551640, 10585263, 10670023, 10880103, 10966033, 11012443, 11098893, 11111111, 11139520, 11289825, 11313133, 11400753, 11448073, 11515031, 11536213, 11748840, 11754613, 11843923, 11892153, 11981983, 12061660, 12204543, 12220131, 12295543, 12326281, 12344683, 12436203, 12662923, 12703860, 12755613, 12805663, 12898873, 13129753, 13179661, 13224133, 13275093, 13368460, 13369993, 13605033, 13701103, 13709280, 13752973, 13849563, 14088763, 14186523, 14231295, 14239303, 14337583, 14408200, 14580943, 14680393, 14734083, 14834053, 14947699, 15081573, 15130480, 15182713, 15237313, 15314745, 15338973, 15500500, 15590653, 15693483, 15748993, 15852343, 15876504, 16108183, 16212703, 16258540, 16269123, 16374163, 16451835, 16634163, 16646656, 16740373, 16777215, 16797703, 16904433, 17040900, 17043521, 17168593, 17276493, 17334733, 17441320, 17443153, 17711473, 17821063, 17880213, 17990323, 18260880, 18262803, 18374083, 18434143, 18545943, 18822583, 18935553, 18996523, 19105720, 19110013, 19390813, 19505473, 19537740, 19567353, 19682533, 19967493, 20155611, 20344611, 20421220, 20425881, 20616141, 20646175, 21109431, 21302841, 21330940, 21386001, 21523360, 21580671, 21795760, 22085301, 22283121, 22368171, 22505575, 22567251, 22745560, 23083221, 23230636, 23285451, 23372391.

Some larger examples :