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centered triangular n.  and  tau n.

First numbers that belong to both sets:

1, 136, 4456, 8104, 15760, 16696, 21064, 22144, 43096, 69016, 70960, 81784, 91144, 105736, 116344, 144616, 162856, 210376, 228736, 232264, 247864, 267760, 332056, 359416, 407944, 433360, 601984, 696664, 723496, 791704, 826960, 833656, 862984, 937336, 982936, 1102960, 1144504, 1178824, 1221760, 1409896, 1543816, 1602184, 1693360, 1702936, 1968256, 2079760, 2183464, 2619544, 2866960, 2933704, 3001216, 3151576, 3350296, 3363760, 3436024, 3495304, 3885736, 4106056, 4120960, 4266424, 4347760, 4363096, 4429864, 4596376, 4696696, 4938616, 4954960, 5567104, 5961064, 6135760, 6153976, 6853360, 6956344, 7060096, 7144960, 7250104, 7590376, 8118904, 8230960, 8252056, 8919424, 8941384, 9058960, 9416296, 10151704, 10253416, 10633360, 10657336, 10785664, 11571760, 11705464, 12085624, 12359656, 12802744, 12943360, 13200184, 13342960, 13369816, 14363896, 14391760, 14540824, 15268936, 15297664, 15760984, 16201624, 16359760, 16518664, 16838776, 17518960, 17817544, 17983360, 18485416, 19026424, 19683760, 19858024, 20596096, 20774344, 20953360, 22009096, 22750696, 23126104, 23314960, 23350456, 23504584, 23694976, 24694960, 25049224, 26680960, 27049144, 27253360, 28743760, 29377576, 30193024, 31279384, 31540216, 31719304, 32162296, 33099760, 33509704, 33552256, 33964984, 34423336, 36051760, 37477504, 37522504, 37762960, 38200744, 38686744, 39467656, 39961624, 40911760, 40958776, 41209984, 41667256, 41968216, 42477544, 42685336, 42733360, 43505416, 45548416, 45813304, 46078960, 46128856, 47199736, 48010960, 48829096, 49602376, 49654144, 50712616, 51044584, 51272344, 51553360, 53309224, 53595760, 54117064, 54405760, 56448136, 56798344, 57334960, 57632104, 58228696, 58884736, 59431096, 60036904, 60398056, 60645784, 62490856, 63423760, 64049536, 64363576, 65369704, 65686960, 68901760, 69819760, 70147624, 71197816, 72130936, 72193360, 73195816, 74479744, 74543176, 76522960, 76587256, 78658984, 79006960, 79705216, 80055496, 81464296, 82462216, 82885384, 83533360, 83891944, 84611416, 85696384, 86127760, 88254856, 89733736, 90175144, 90850960, 91224904, 91295104, 93555760, 93935224, 95772136, 97312456, 97384960, 97699456, 98475760, 101290960, 102477736, 102800344, 103671424, 104872024, 106407760, 108923944, 109333360, 110488960, 112220776, 113052664, 114646960, 115909336, 116834176, 117682960, 118454824, 120167176, 120677896, 122758744, 123193360, 123274936, 124064896, 126257176, 126339760, 130783360, 132046960, 132131416, 133939576, 135303760, 135760024, 136131304, 138427264, 138513736, 139437784, 141207760, 144574960, 145518976, 145992136, 146377144, 150675760, 150765976, 153576064, 153667144, 154062136, 154153360, 154640344, 160450960, 161041024, 162536536, 163537384, 164038960, 164950024.

Some larger examples :