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centered nonagonal n.  and  equidigital n.

First numbers that belong to both sets:

1, 10, 1081, 1225, 1711, 1891, 2485, 2701, 3403, 4753, 10585, 12403, 13861, 15931, 18721, 31375, 32896, 100576, 104653, 108811, 110215, 114481, 120295, 124750, 126253, 140185, 146611, 153181, 158203, 166753, 171991, 180901, 188191, 193753, 205120, 216811, 218791, 226801, 234955, 251695, 258121, 269011, 275653, 286903, 341551, 344035, 351541, 354061, 364231, 371953, 385003, 392941, 439453, 470935, 482653, 497503, 524800, 780625, 1034641, 1056331, 1073845, 1091503, 1104841, 1127251, 1145341, 1159003, 1181953, 1309771, 1314631, 1348903, 1353835, 1368685, 1373653, 1408681, 1537381, 1553203, 1558495, 1574425, 1644391, 1660753, 1710325, 1755001, 1771903, 1794565, 1817371, 1869211, 1886653, 1933561, 1963171, 1987021, 2096128, 2414503, 3126250, 3544453, 3946645, 4881250, 5649841, 5884165, 6060421, 6420736, 6835753, 6924781, 9757153, 10037440, 10064341, 10131751, 10185841, 10280845, 10335331, 10389961, 10403641, 10444735, 10499653, 10554715, 10679131, 10916128, 10944181, 11000395, 11056753, 11127403, 11212480, 11283625, 11297881, 11354995, 11455291, 11469655, 11512801, 11584891, 11686195, 11700703, 11860885, 11934055, 11992753, 12051595, 12066328, 12095821, 12169711, 12214153, 12273535, 12288403, 12347965, 12497500, 12512503, 12814453, 12890503, 12936241, 12951505, 12997351, 13012651, 13073941, 13243231, 13429153, 13569445, 13679065, 13694761, 14010571, 14169826, 14185801, 14201785, 14442625, 14507191, 14571901, 14636755, 14652991, 14783203, 14963185, 14996026, 15028903, 15144256, 15160771, 15226921, 15293215, 15442903, 15509665, 15559831, 15576571, 15778153, 15896341, 16185205, 16253551, 16304905, 16373503, 16528375, 16597441, 16718653, 16857721, 16944931, 17207911, 17225515, 17278381, 17331328, 17366671, 17561701, 17632891, 17919091, 17991001, 18063055, 18081091, 18225703, 18280081, 18443701, 18736381, 18791515, 18809911, 18865153, 19012861, 19235503, 19272736, 19328653, 19403335, 19665856, 19703503, 19760041, 19835551, 19911205.