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centered nonagonal n.  and  Duffinian n.

First numbers that belong to both sets:

55, 253, 325, 595, 1081, 1225, 1711, 2485, 3403, 3655, 5671, 7021, 7381, 8515, 8911, 10153, 11935, 13861, 14365, 15931, 20503, 21115, 23005, 23653, 25651, 28441, 31375, 32131, 34453, 37675, 44551, 45451, 48205, 52003, 52975, 55945, 60031, 64261, 65341, 68635, 73153, 74305, 82621, 87571, 92665, 97903, 108811, 110215, 114481, 115921, 120295, 121771, 126253, 127765, 132355, 133903, 138601, 140185, 144991, 153181, 158203, 159895, 171991, 179101, 186355, 193753, 195625, 201295, 208981, 216811, 224785, 232903, 243253, 249571, 258121, 260281, 266815, 275653, 293761, 303031, 305371, 314821, 322003, 331705, 334153, 341551, 351541, 354061, 361675, 371953, 374545, 392941, 403651, 406351, 417241, 425503, 428275, 436645, 459361, 462241, 470935, 482653, 506521, 518671, 530965, 543403, 555985, 568711, 584821, 607753, 621055, 634501, 651511, 661825, 679195, 689725, 693253, 703891, 747253, 750925, 776881, 791911, 795691, 807085, 822403, 826255, 837865, 853471, 869221, 889111, 901153, 917335, 933661, 937765, 983503, 1000405, 1004653, 1017451, 1034641, 1073845, 1091503, 1104841, 1122751, 1127251, 1140805, 1145341, 1159003, 1181953, 1214461, 1233235, 1237951, 1252153, 1256905, 1290421, 1309771, 1329265, 1334161, 1348903, 1353835, 1368685, 1388611, 1408681, 1413721, 1449253, 1454365, 1490401, 1511191, 1532125, 1553203, 1558495, 1574425, 1595791, 1617301, 1638955, 1644391, 1660753, 1666225, 1682695, 1688203, 1704781, 1710325, 1727011, 1749385, 1771903, 1817371, 1823095, 1840321, 1846081, 1863415, 1886653, 1910035, 1915903, 1933561, 1957231, 1963171, 2053351, 2077741, 2083861, 2126953, 2151775, 2158003, 2176741, 2201851, 2208151, 2227105, 2252503, 2258875, 2329561, 2362051, 2381653, 2434321, 2440945, 2460871, 2487565, 2494261, 2514403, 2548153, 2568511, 2650753, 2657665, 2685403, 2706301, 2713285, 2762425, 2790703, 2847691, 2883601, 2905255, 2912491, 2934253, 2941525, 2963395, 2992681, 3022111, 3029491, 3081403, 3088855, 3118753, 3141271, 3148795, 3171421, 3201715, 3232153, 3262735, 3293461, 3301165, 3324331, 3332071, 3355345, 3386503, 3394315, 3417805, 3449251, 3488761, 3520531, 3544453, 3552445, 3576475, 3608641, 3640951, 3673405, 3706003, 3738745, 3771631, 3804661, 3812941, 3837835, 3846151, 3871153, 3938221, 3946645, 3971971, 4039903, 4074085, 4108411, 4142881, 4212253, 4247155, 4282201, 4317391.

Some larger examples :