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lucky n.  and  triangular n.

First numbers that belong to both sets:

1, 3, 15, 21, 105, 171, 231, 741, 903, 1275, 1485, 1711, 2211, 2415, 3003, 3403, 3655, 4095, 4465, 4851, 5151, 5253, 5671, 7503, 8001, 8515, 10153, 10585, 10731, 11781, 13203, 13695, 13861, 17391, 18145, 18915, 19503, 21115, 22155, 22791, 24531, 25425, 26565, 28203, 32385, 33153, 33411, 34191, 34453, 35511, 38503, 39903, 41905, 43071, 44551, 47895, 48205, 49141, 51681, 52975, 53301, 54285, 57291, 58311, 60031, 61425, 63903, 65341, 70125, 71631, 79003, 79401, 85491, 87153, 87571, 90951, 92665, 96141, 99235, 104653, 106491, 106953, 112101, 114003, 114481, 115921, 121771, 125751, 138601, 140185, 142845, 146611, 155403, 162165, 162735, 166753, 171991, 173755, 174345, 176121, 176715, 179101, 183921, 186355, 196251, 210925, 211575, 219453, 224785, 232221, 235641, 241165, 246753, 254541, 255255, 257403, 258121, 266085, 269011, 280875, 284635, 289941, 292995, 299925, 303031, 305371, 318801, 322003, 331705, 334971, 338253, 340725, 347361, 350703, 354903, 371953, 385003, 396495, 400065, 410871, 413595, 428275, 435711, 436645, 440391, 444153, 451725, 454581, 455535, 493521, 502503, 506521, 510555, 514605, 522753, 535095, 547581, 555985, 563391, 568711, 576201, 577275, 584821, 585903, 597871, 598965, 602253, 616605, 633375, 639015, 642411, 652653, 679195, 680361, 699153, 723003, 727821, 736291, 747253, 755835, 785631, 790653, 795691, 805815, 817281, 821121, 846951, 848253, 853471, 862641, 863955, 873181, 874503, 890445, 905185, 944625, 965355, 972315, 983503, 1010331, 1021735, 1033203, 1044735, 1063611, 1067991, 1081185, 1103355, 1104841, 1128753, 1177345, 1183491, 1206681, 1225395, 1244253, 1314631, 1322751, 1342341, 1380291, 1386945, 1442451, 1454365, 1483503, 1530375, 1560261, 1574425, 1581531, 1594005, 1629915, 1658931, 1660753, 1668051, 1695561, 1712175, 1717731, 1719585, 1727011, 1734453, 1741911, 1747515, 1749385, 1764381, 1779441, 1807851, 1809753, 1817371, 1855701, 1861485, 1863415, 1910035, 1989015, 2011015, 2019045, 2035153, 2053351, 2077741, 2094081, 2118711, 2149701, 2151775, 2158003, 2160081, 2166321, 2174655, 2183005, 2224995, 2227105, 2244021, 2258875, 2269515, 2293011, 2295153, 2329561, 2346861, 2362051, 2364225, 2370753, 2372931, 2379471, 2388205, 2476425.

Some larger examples :