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hoax n.  and  triangular n.

First numbers that belong to both sets:

136, 861, 4656, 5253, 7503, 9180, 11476, 12880, 16653, 28680, 70876, 72771, 84255, 92235, 94395, 118828, 120786, 130816, 132870, 135460, 141778, 157641, 189420, 204480, 246753, 253828, 258840, 263901, 272691, 278631, 283128, 299151, 314028, 334971, 342378, 361675, 375411, 385881, 388521, 408156, 424581, 428275, 455535, 480690, 481671, 483636, 564453, 588070, 618828, 723003, 788140, 804546, 839160, 844350, 866586, 897130, 977901, 993345, 1047628, 1049076, 1060696, 1062153, 1084128, 1134771, 1152921, 1166628, 1168156, 1191196, 1228528, 1234806, 1237951, 1317876, 1343980, 1362075, 1433971, 1452660, 1457778, 1495585, 1528626, 1590436, 1597578, 1666225, 1679028, 1680861, 1738180, 1792671, 1805950, 1855701, 1876953, 1931595, 2089990, 2137278, 2220778, 2396955, 2440945, 2458653, 2757726, 2828631, 2862028, 2878800, 2890810, 2924571, 2941525, 2968266, 3126250, 3176460, 3255076, 3257628, 3278080, 3314025, 3467661, 3504628, 3597903, 3635556, 3716901, 3722356, 3733278, 3757911, 3896236, 3904615, 3935415, 4079796, 4168828, 4408965, 4444671, 4643628, 4815856, 4822065, 4843828, 4887501, 4890628, 4925091, 4943940, 5076891, 5096028, 5153655, 5335011, 5351356, 5492955, 5586153, 5808936, 6154786, 6165316, 6295926, 6420736, 6546771, 6652128, 6659425, 6725278, 6943401, 6984453, 7006896, 7051890, 7119651, 7244721, 7305753, 7405476, 7436296, 7536903, 7583565, 7595253, 7850703, 7858630, 7946091, 8058105, 8126496, 8191128, 8211378, 8223540, 8280415, 8284485, 8304850, 8341570, 8345655, 8398851, 8501626, 8885220, 8944335, 9033375, 9139950, 9281586, 9359301, 9459075, 9859020, 10068828, 10660653, 10799628, 10906785, 10925475, 10981641, 10991016, 10995705, 11075571, 11378835, 11787940, 11938941, 12031965, 12149985, 12258676, 12328095, 12527515, 12597690, 12931155, 13238085, 13274128, 13294746, 13341195, 13377378, 13387725, 13398076, 13590291, 13673835, 13720941, 13736661, 13873278, 13968255, 13973541, 14761461, 14788641, 14804961, 14848525, 14864878, 14870331, 15056328, 15149760, 15188316, 15276628, 15924546, 16247850, 16276365, 16933290, 17484741, 17567628, 17668540, 17739946, 17757820, 17787630, 17841351, 18045028, 18431556, 18742503, 18920476, 18988203, 19056051, 19434495, 19509381, 19565640, 19892278, 19942770, 20259795, 20604990, 20701395, 20881953, 20985481, 21225870, 21264981, 21809710, 21889036, 22074690, 22596003, 22845420, 23252790, 23560680, 23656881, 23663760, 23732605, 23918986, 23981275, 23988201, 24580566, 24728028, 25386375, 25507653, 25794153, 25866028, 25938003, 26053371, 26393745, 26495560, 26677860.

Some larger examples :