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decagonal n.  and  happy n.

First numbers that belong to both sets:

1, 10, 637, 2425, 4257, 4522, 10251, 11077, 11502, 13282, 17226, 21682, 22275, 32130, 32851, 38122, 38907, 39700, 42952, 48070, 51642, 54405, 55342, 57240, 58201, 62125, 63126, 65152, 68251, 87172, 95635, 99382, 105787, 112392, 126202, 140812, 149962, 157807, 187705, 205435, 207252, 218322, 222076, 235467, 241326, 243295, 249250, 257302, 263425, 273790, 280105, 288637, 303876, 308302, 324045, 328615, 403542, 411201, 426735, 429352, 458667, 464101, 503035, 508725, 534726, 543537, 567385, 570402, 594826, 597915, 604117, 645210, 654885, 694305, 711070, 717832, 734877, 745200, 748657, 755595, 815860, 823102, 830376, 837682, 845020, 867226, 889720, 935572, 947215, 1002501, 1047040, 1051137, 1084201, 1092547, 1105126, 1139022, 1160467, 1164780, 1208350, 1221577, 1226002, 1239325, 1284255, 1297890, 1311597, 1325376, 1353150, 1385917, 1428622, 1433407, 1438200, 1525842, 1641601, 1662165, 1688050, 1703677, 1719376, 1740420, 1798951, 1804320, 1842127, 1853001, 1935576, 2019951, 2037042, 2071440, 2094532, 2106126, 2117752, 2141100, 2158695, 2164576, 2176362, 2283876, 2289925, 2295982, 2302047, 2308120, 2375451, 2412585, 2431260, 2450007, 2525715, 2544822, 2557600, 2564001, 2720025, 2733235, 2739852, 2746477, 2853565, 2955820, 3038920, 3066876, 3116107, 3165730, 3215745, 3258927, 3295132, 3368142, 3434535, 3479157, 3509065, 3524067, 3531580, 3722005, 3752937, 3799575, 3877945, 3933280, 3965076, 4029052, 4061232, 4109742, 4134105, 4166701, 4257000, 4314967, 4364965, 4533705, 4559292, 4653727, 4671001, 4705645, 4731712, 4766580, 4827907, 4889626, 4951737, 5005287, 5095177, 5167665, 5249826, 5304960, 5388201, 5406787, 5462737, 5490820, 5584950, 5632315, 5679880, 5746807, 5940187, 5959701, 6008626, 6570250, 6621615, 6797752, 6934005, 6955087, 6965640, 7007932, 7114222, 7146265, 7178380, 7264372, 7318377, 7514451, 7580385, 7591402, 7679826, 7735351, 7746480, 7914375, 7925632, 8038642, 8072701, 8084070, 8129626, 8152452, 8221122, 8267062, 8278567, 8463735, 8498682, 8580505, 8662720, 8698075, 8864017, 8887851, 8947576, 9176355, 9285732, 9383500, 9395757, 9506430, 9543465, 9568195, 9605350, 9704782, 9767187, 9854890, 9968227, 9980860.