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hexagonal n.  and  Ulam n.

First numbers that belong to both sets:

1, 6, 28, 861, 1035, 1431, 1770, 8128, 11781, 15400, 20301, 22791, 25425, 37950, 48516, 49141, 54285, 58996, 61075, 61776, 67528, 102831, 105570, 110215, 114960, 118828, 134940, 135981, 139128, 144453, 152076, 162165, 177310, 186966, 198135, 201930, 205761, 228150, 232221, 243253, 257403, 263175, 302253, 324415, 383250, 397386, 408156, 417241, 424581, 437580, 456490, 471906, 473851, 479710, 567645, 653796, 662976, 695610, 726615, 736291, 743590, 746031, 773146, 793170, 831405, 841753, 883785, 910575, 926841, 937765, 1001820, 1041846, 1100386, 1121253, 1133265, 1142316, 1228528, 1272810, 1288815, 1360425, 1370340, 1420455, 1523385, 1558495, 1576200, 1590436, 1971105, 2007006, 2051325, 2059435, 2096128, 2116653, 2137278, 2149701, 2153850, 2191371, 2237670, 2271646, 2288730, 2293011, 2331720, 2454220, 2471976, 2480878, 2512161, 2534626, 2745996, 2760075, 2783620, 2835771, 2859636, 2874003, 2883601, 2956096, 2985346, 3148795, 3224530, 3326910, 3337236, 3478203, 3488761, 3515226, 3552445, 3649051, 3692403, 3785376, 3801903, 4003035, 4186171, 4191960, 4250070, 4285128, 4302711, 4462578, 4522528, 4643628, 4853170, 4890628, 4909411, 4928230, 4991220, 5086455, 5144028, 5182590, 5201925, 5286126, 5344815, 5430160, 5456556, 5549446, 5562780, 5670028, 5744355, 5921961, 5997916, 6123250, 6193440, 6278196, 6306576, 6342141, 6363528, 6674031, 6872778, 7044381, 7112106, 7240915, 7256145, 7455591, 7681240, 7767711, 7775596, 7918210, 8006001, 8070153, 8370186, 8443995, 8485140, 8509875, 8542911, 8642403, 8650720, 8675695, 8700706, 8826301, 9003646, 9157060, 9217071, 9260056, 9294516, 9380946, 9459075, 9669003, 9686601, 9748320, 9827961.