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centered nonagonal n.  and  hexagonal n.

First numbers that belong to both sets:

1, 28, 91, 190, 325, 496, 703, 946, 1225, 1540, 1891, 2278, 2701, 3160, 3655, 4186, 4753, 5356, 5995, 6670, 7381, 8128, 8911, 9730, 10585, 11476, 12403, 13366, 14365, 15400, 16471, 17578, 18721, 19900, 21115, 22366, 23653, 24976, 26335, 27730, 29161, 30628, 32131, 33670, 35245, 36856, 38503, 40186, 41905, 43660, 45451, 47278, 49141, 51040, 52975, 54946, 56953, 58996, 61075, 63190, 65341, 67528, 69751, 72010, 74305, 76636, 79003, 81406, 83845, 86320, 88831, 91378, 93961, 96580, 99235, 101926, 104653, 107416, 110215, 113050, 115921, 118828, 121771, 124750, 127765, 130816, 133903, 137026, 140185, 143380, 146611, 149878, 153181, 156520, 159895, 163306, 166753, 170236, 173755, 177310, 180901, 184528, 188191, 191890, 195625, 199396, 203203, 207046, 210925, 214840, 218791, 222778, 226801, 230860, 234955, 239086, 243253, 247456, 251695, 255970, 260281, 264628, 269011, 273430, 277885, 282376, 286903, 291466, 296065, 300700, 305371, 310078, 314821, 319600, 324415, 329266, 334153, 339076, 344035, 349030, 354061, 359128, 364231, 369370, 374545, 379756, 385003, 390286, 395605, 400960, 406351, 411778, 417241, 422740, 428275, 433846, 439453, 445096, 450775, 456490, 462241, 468028, 473851, 479710, 485605, 491536, 497503, 503506, 509545, 515620, 521731, 527878, 534061, 540280, 546535, 552826, 559153, 565516, 571915, 578350, 584821, 591328, 597871, 604450, 611065, 617716, 624403, 631126, 637885, 644680, 651511, 658378, 665281, 672220, 679195, 686206, 693253, 700336, 707455, 714610, 721801, 729028, 736291, 743590, 750925, 758296, 765703, 773146, 780625, 788140, 795691, 803278, 810901, 818560, 826255, 833986, 841753, 849556, 857395, 865270, 873181, 881128, 889111, 897130, 905185, 913276, 921403, 929566, 937765, 946000, 954271, 962578, 970921, 979300, 987715, 996166, 1004653, 1013176, 1021735, 1030330, 1038961, 1047628, 1056331, 1065070, 1073845, 1082656, 1091503, 1100386, 1109305, 1118260, 1127251, 1136278, 1145341, 1154440, 1163575, 1172746, 1181953, 1191196, 1200475, 1209790, 1219141, 1228528, 1237951, 1247410, 1256905, 1266436, 1276003, 1285606, 1295245, 1304920, 1314631, 1324378, 1334161, 1343980, 1353835, 1363726, 1373653, 1383616, 1393615, 1403650.

Some larger examples :