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centered octagonal n.  and  evil n.

First numbers that belong to both sets:

9, 169, 225, 441, 729, 1369, 2025, 2209, 2809, 3249, 3721, 3969, 4761, 5329, 6561, 6889, 8649, 9801, 11025, 11449, 11881, 12321, 13225, 14161, 15129, 17689, 18769, 19881, 22801, 24025, 25281, 25921, 27225, 29241, 31329, 33489, 34969, 36481, 38025, 39601, 41209, 42025, 42849, 44521, 45369, 47961, 48841, 54289, 56169, 58081, 60025, 62001, 64009, 65025, 68121, 70225, 72361, 74529, 76729, 78961, 82369, 83521, 84681, 85849, 87025, 89401, 91809, 96721, 99225, 100489, 103041, 106929, 109561, 110889, 113569, 114921, 120409, 128881, 130321, 133225, 134689, 136161, 137641, 142129, 145161, 149769, 152881, 157609, 159201, 162409, 168921, 170569, 172225, 173889, 175561, 182329, 190969, 194481, 196249, 199809, 203401, 205209, 207025, 210681, 212521, 214369, 216225, 221841, 225625, 227529, 233289, 239121, 241081, 245025, 249001, 253009, 257049, 267289, 271441, 275625, 279841, 284089, 286225, 292681, 305809, 308025, 310249, 328329, 332929, 344569, 349281, 351649, 358801, 366025, 368449, 370881, 378225, 380689, 385641, 390625, 393129, 398161, 408321, 410881, 421201, 426409, 429025, 431649, 434281, 455625, 469225, 471969, 483025, 494209, 499849, 502681, 505521, 508369, 514089, 519841, 522729, 531441, 537289, 540225, 546121, 549081, 561001, 564001, 573049, 576081, 582169, 588289, 594441, 600625, 609961, 613089, 622521, 632025, 641601, 651249, 657721, 660969, 667489, 674041, 677329, 683929, 687241, 693889, 703921, 707281, 710649, 714025, 717409, 724201, 727609, 731025, 741321, 744769, 748225, 751689, 762129, 769129, 779689, 783225, 786769, 797449, 808201, 819025, 829921, 833569, 837225, 874225, 877969, 885481, 893025, 896809, 912025, 915849, 919681, 942841, 946729, 950625, 954529, 958441, 966289, 978121, 986049, 994009, 998001, 1010025, 1018081, 1026169, 1034289, 1042441, 1046529, 1058841, 1067089, 1075369, 1083681, 1092025, 1096209, 1108809, 1117249, 1125721, 1129969, 1138489, 1147041, 1151329, 1155625, 1159929, 1164241, 1168561, 1185921, 1190281, 1194649, 1199025, 1203409, 1212201, 1221025, 1234321, 1238769, 1270129, 1274641, 1279161, 1288225, 1292769, 1297321, 1301881, 1311025, 1315609, 1324801, 1329409, 1338649, 1343281, 1347921, 1375929, 1385329, 1390041, 1394761, 1399489.

Some larger examples :