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centered octagonal n.  and  odious n.

First numbers that belong to both sets:

1, 25, 49, 81, 121, 289, 361, 529, 625, 841, 961, 1089, 1225, 1521, 1681, 1849, 2401, 2601, 3025, 3481, 4225, 4489, 5041, 5625, 5929, 6241, 7225, 7569, 7921, 8281, 9025, 9409, 10201, 10609, 12769, 13689, 14641, 15625, 16129, 16641, 17161, 18225, 19321, 20449, 21025, 21609, 22201, 23409, 24649, 26569, 27889, 28561, 29929, 30625, 32041, 32761, 34225, 35721, 37249, 38809, 40401, 43681, 46225, 47089, 49729, 50625, 51529, 52441, 53361, 55225, 57121, 59049, 61009, 63001, 66049, 67081, 69169, 71289, 73441, 75625, 77841, 80089, 81225, 88209, 90601, 93025, 94249, 95481, 97969, 101761, 104329, 105625, 108241, 112225, 116281, 117649, 119025, 121801, 123201, 124609, 126025, 127449, 131769, 139129, 140625, 143641, 146689, 148225, 151321, 154449, 156025, 160801, 164025, 165649, 167281, 177241, 178929, 180625, 184041, 185761, 187489, 189225, 192721, 198025, 201601, 208849, 218089, 219961, 223729, 229441, 231361, 235225, 237169, 243049, 247009, 251001, 255025, 259081, 261121, 263169, 265225, 269361, 273529, 277729, 281961, 288369, 290521, 294849, 297025, 299209, 301401, 303601, 312481, 314721, 316969, 319225, 321489, 323761, 326041, 330625, 335241, 337561, 339889, 342225, 346921, 354025, 356409, 361201, 363609, 373321, 375769, 383161, 388129, 395641, 400689, 403225, 405769, 413449, 416025, 418609, 423801, 436921, 439569, 442225, 444889, 447561, 450241, 452929, 458329, 461041, 463761, 466489, 474721, 477481, 480249, 485809, 488601, 491401, 497025, 511225, 516961, 525625, 528529, 534361, 543169, 552049, 555025, 558009, 567009, 570025, 579121, 585225, 591361, 597529, 603729, 606841, 616225, 619369, 625681, 628849, 635209, 638401, 644809, 648025, 654481, 664225, 670761, 680625, 690561, 697225, 700569, 720801, 734449, 737881, 755161, 758641, 765625, 772641, 776161, 790321, 793881, 801025, 804609, 811801, 815409, 822649, 826281, 840889, 844561, 848241, 851929, 855625, 859329, 863041, 866761, 870489, 881721, 889249, 900601, 904401, 908209, 923521, 927369, 931225, 935089, 938961, 962361, 970225, 974169, 982081, 990025, 1002001, 1006009, 1014049, 1022121, 1030225, 1038361, 1050625, 1054729, 1062961.

Some larger examples :