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Smith n.  and  triangular n.

First numbers that belong to both sets:

378, 666, 861, 2556, 5253, 7503, 10296, 16653, 27261, 28920, 29890, 32896, 46056, 72771, 84255, 85905, 92235, 94395, 120786, 132870, 141778, 157641, 215496, 328455, 345696, 385881, 386760, 396495, 424581, 529935, 533028, 588070, 654940, 682696, 683865, 723003, 778128, 866586, 885115, 897130, 941878, 959805, 977901, 993345, 1082656, 1134771, 1234806, 1398628, 1457778, 1466328, 1495585, 1528626, 1570878, 1597578, 1633528, 1680861, 1792671, 1875016, 1876953, 1925703, 1931595, 1983036, 2087946, 2089990, 2137278, 2273778, 2351196, 2396955, 2458653, 2692360, 2828631, 2859636, 2890810, 2924571, 2968266, 3296028, 3378700, 3383901, 3451878, 3467661, 3579150, 3654456, 3733278, 3757911, 3904615, 3935415, 4119885, 4444671, 4710915, 4887501, 4925091, 5492955, 5586153, 5592840, 5815755, 6725278, 6984453, 7051890, 7486515, 7505875, 7536903, 7583565, 7850703, 7858630, 8090253, 8158780, 8211378, 8280415, 8284485, 8341570, 8390656, 8398851, 8485140, 8501626, 8982441, 9281586, 9359301, 9541896, 9651421, 9677800, 10158778, 10330785, 10981641, 10986328, 11541610, 11556028, 12149985, 12159846, 12328095, 12527515, 12597690, 12926070, 13027960, 13155885, 13377378, 13559028, 13590291, 13736661, 13873278, 13968255, 13973541, 14063556, 14761461, 14799520, 14804961, 14864878, 14881240, 15570990, 15598905, 15671601, 15918903, 16950753, 17190316, 17478828, 17573556, 17739946, 17787630, 17841351, 18389080, 18742503, 18945090, 18988203, 19006695, 19043706, 19359753, 19378425, 19434495, 19892278, 19942770, 19955403, 20259795, 20791576, 20817378, 20985481, 21264981, 21809710, 22074690, 22656546, 23177836, 23252790, 23334696, 23464675, 23656881, 23918986, 23988201, 24897096, 25507653, 25693696, 25988445, 26386480, 26393745, 26553828, 26846128, 27442936, 27762426, 27807153, 28278960, 28369278, 28489926, 28535235, 29196261, 29464326, 29518086, 29756755, 30556653, 30799476, 30846585, 31892091, 32421378, 32453596, 32477770, 32598775, 32768560, 33247935, 33386706, 33648706, 33812976, 34084896, 35141536, 35866215, 36359128, 36495696, 36572628, 37493470, 37858051, 37936405, 38574936, 39271953, 40396566, 40829166, 41518828, 41527941, 42168336, 42730390, 42943278, 43407903, 44816778, 45481953, 45873831, 45892990, 46238536, 46334751, 46566075, 47799753, 47848653, 47917155, 48348861, 48447246, 49059465, 49426653, 49895055, 49995000, 50095045, 50275378, 50556540, 50949465, 51070671, 51485878, 51689028, 51719535, 52608153, 52947195, 53008956, 53194455, 53649261, 53908536, 54376806, 54575128, 55172260, 56068755, 56588841, 56705925, 56865780, 56951128, 56993826, 57154086, 57164778, 57228951, 57239650, 57357405.

Some larger examples :