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hexagonal n.  and  lucky n.

First numbers that belong to both sets:

1, 15, 231, 2415, 3003, 3655, 5151, 10585, 11781, 13695, 19503, 21115, 22791, 24531, 25425, 28203, 33153, 34191, 38503, 41905, 43071, 47895, 49141, 51681, 52975, 54285, 58311, 63903, 65341, 79003, 85491, 87153, 99235, 104653, 106491, 112101, 114003, 115921, 121771, 125751, 140185, 146611, 155403, 162165, 166753, 173755, 176121, 210925, 232221, 254541, 257403, 266085, 269011, 280875, 289941, 292995, 305371, 340725, 347361, 350703, 385003, 413595, 428275, 435711, 454581, 493521, 563391, 576201, 584821, 597871, 602253, 633375, 642411, 679195, 736291, 755835, 785631, 790653, 795691, 805815, 821121, 846951, 862641, 873181, 905185, 965355, 1010331, 1021735, 1033203, 1044735, 1067991, 1103355, 1206681, 1225395, 1244253, 1314631, 1380291, 1386945, 1454365, 1530375, 1594005, 1629915, 1658931, 1695561, 1717731, 1747515, 1807851, 1861485, 2011015, 2019045, 2035153, 2149701, 2158003, 2166321, 2174655, 2183005, 2224995, 2258875, 2293011, 2362051, 2370753, 2379471, 2388205, 2476425, 2566245, 2584401, 2620905, 2666895, 2722611, 2741311, 2750685, 2769481, 2788341, 2835771, 2864421, 2922153, 2931831, 2951235, 3009831, 3039345, 3128751, 3148795, 3280641, 3332071, 3342405, 3478203, 3531153, 3703281, 3779875, 3868371, 3991725, 4003035, 4025703, 4059825, 4082653, 4163055, 4209351, 4279275, 4290985, 4432753, 4444671, 4480521, 4760155, 4884375, 4896885, 5035551, 5189031, 5214835, 5227761, 5305653, 5357901, 5556111, 5596185, 5622981, 5649841, 5717271, 5785101, 5825991, 5990991, 6004845, 6074355, 6186403, 6200481, 6214575, 6256953, 6427905, 6471003, 6485401, 6543153, 6557631, 6586635, 6747301, 6776721, 6984453, 6999411, 7089495, 7104565, 7225701, 7378561, 7548555, 7783485, 8006001, 8070153, 8215431, 8280415, 8296701, 8542911, 8625781, 8742471, 8792721, 8826301, 8910531, 8961261, 8995161, 9131401, 9546265, 9845703, 9916831, 9988215.