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pentagonal n.  and  wasteful n.

First numbers that belong to both sets:

12, 22, 51, 70, 92, 117, 176, 210, 247, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2882, 3015, 3151, 3290, 3432, 3725, 3876, 4030, 4347, 4510, 4676, 4845, 5017, 5192, 5370, 5551, 5735, 5922, 6112, 6305, 6501, 6700, 6902, 7107, 7315, 7526, 7740, 7957, 8177, 8400, 8626, 8855, 9087, 9322, 9560, 9801, 10292, 10542, 10795, 11310, 11572, 12105, 12376, 12650, 12927, 13490, 13776, 14652, 14950, 15251, 15555, 15862, 16172, 16485, 17120, 17442, 17767, 18095, 18426, 18760, 19097, 19437, 19780, 20126, 20475, 21182, 21540, 21901, 22632, 23002, 23375, 23751, 24130, 24897, 25285, 25676, 26070, 26467, 27270, 27676, 28085, 28497, 28912, 29330, 29751, 30175, 30602, 31032, 31465, 31901, 32340, 32782, 33227, 33675, 34126, 34580, 35037, 35497, 35960, 36426, 36895, 37367, 37842, 38320, 38801, 39772, 40262, 40755, 41750, 42252, 42757, 43265, 43776, 44290, 44807, 45327, 45850, 46376, 46905, 47437, 47972, 48510, 49051, 49595, 50142, 50692, 51245, 51801, 52360, 52922, 53487, 54055, 54626, 55200, 55777, 56940, 57526, 58115, 58707, 59302, 59900, 60501, 61105, 61712, 62322, 62935, 63551, 64170, 64792, 65417, 66045, 66676, 67310, 67947, 68587, 69230, 69876, 70525, 71177, 71832, 72490, 73151, 73815, 74482, 75152, 75825, 76501, 77180, 77862, 79235, 79926, 80620, 81317, 82017, 82720, 83426, 84135, 84847, 85562, 86280, 87001, 87725, 88452, 89182, 89915, 90651, 91390, 92132, 92877, 93625, 94376, 95130, 95887, 96647, 97410, 98176, 98945, 99717, 100492, 101270, 102051, 102835, 103622, 104412, 106800, 107602, 108407, 110026, 110840, 111657, 113300, 114126, 115787, 116622, 117460, 119145, 119992, 120842, 121695, 122551, 123410, 124272, 126005, 126876, 130390, 131276, 132165, 133057, 133952, 134850, 135751, 136655, 137562, 138472, 140301, 141220, 142142, 143067, 144926, 145860, 148680, 150575, 152482, 153440, 154401, 155365, 156332, 158275.

Some larger examples :