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centered nonagonal n.  and  evil n.

First numbers that belong to both sets:

10, 136, 190, 325, 703, 946, 1711, 2080, 2278, 2701, 2926, 4465, 5050, 6328, 6670, 7381, 8911, 9730, 10153, 11026, 11935, 14878, 15400, 15931, 16471, 17578, 19306, 20503, 22366, 23005, 23653, 31375, 32896, 33670, 35245, 36046, 36856, 37675, 39340, 40186, 41905, 42778, 44551, 45451, 50086, 52003, 52975, 54946, 55945, 57970, 60031, 61075, 62128, 69751, 70876, 73153, 75466, 83845, 85078, 86320, 87571, 90100, 96580, 99235, 100576, 101926, 103285, 106030, 107416, 108811, 110215, 113050, 115921, 117370, 120295, 121771, 127765, 133903, 140185, 141778, 146611, 153181, 156520, 158203, 163306, 165025, 166753, 170236, 177310, 179101, 180901, 182710, 191890, 195625, 197506, 199396, 207046, 208981, 212878, 216811, 222778, 226801, 239086, 241165, 245350, 247456, 249571, 255970, 260281, 275653, 277885, 284635, 291466, 298378, 305371, 307720, 310078, 312445, 314821, 317206, 334153, 336610, 349030, 354061, 369370, 374545, 382375, 387640, 395605, 403651, 411778, 417241, 419986, 422740, 428275, 433846, 436645, 442270, 453628, 456490, 465130, 473851, 479710, 488566, 494515, 497503, 503506, 506521, 518671, 524800, 527878, 534061, 537166, 540280, 549676, 552826, 559153, 562330, 565516, 568711, 575128, 578350, 588070, 594595, 604450, 634501, 637885, 641278, 648091, 665281, 668746, 686206, 689725, 696790, 703891, 707455, 714610, 721801, 725410, 732655, 736291, 739936, 743590, 750925, 758296, 765703, 769420, 773146, 776881, 784378, 788140, 791911, 795691, 799480, 810901, 814726, 822403, 826255, 833986, 837865, 853471, 857395, 869221, 873181, 889111, 893116, 897130, 909226, 917335, 921403, 925480, 929566, 954271, 962578, 970921, 975106, 991936, 1000405, 1004653, 1017451, 1026028, 1043290, 1051975, 1069453, 1091503, 1100386, 1113778, 1118260, 1127251, 1131760, 1136278, 1140805, 1145341, 1149886, 1163575, 1168156, 1177345, 1186570, 1200475, 1205128, 1223830, 1228528, 1233235, 1237951, 1247410, 1266436, 1280800, 1314631, 1324378, 1329265, 1334161, 1339066, 1348903, 1353835, 1358776, 1378630, 1383616, 1388611, 1393615, 1413721, 1423828, 1428895, 1433971, 1449253, 1454365, 1459486, 1474903, 1480060, 1500778, 1505980, 1511191, 1526878, 1532125, 1558495, 1563796, 1569106, 1579753, 1585090, 1601155, 1606528.

Some larger examples :