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centered heptagonal n.  and  odious n.

First numbers that belong to both sets:

1, 8, 22, 148, 253, 316, 386, 463, 638, 841, 953, 1072, 1471, 1618, 1772, 1933, 2101, 2276, 2647, 2843, 3697, 3928, 4411, 4663, 4922, 5461, 6028, 6931, 7246, 7897, 8576, 9283, 9647, 10781, 11572, 12391, 13238, 13672, 14113, 14561, 15016, 15478, 15947, 16423, 19951, 21022, 22681, 23248, 24991, 25586, 26188, 28036, 29947, 30598, 31256, 31921, 33272, 34651, 35351, 39698, 40447, 44297, 46691, 49148, 49981, 50821, 53383, 54251, 57793, 58696, 59606, 61447, 64261, 65213, 66172, 67138, 68111, 69091, 70078, 72073, 75118, 76147, 78226, 79276, 82468, 84631, 85723, 91288, 92422, 95866, 99373, 100556, 101746, 102943, 106576, 111518, 114031, 115298, 119141, 123047, 124363, 127016, 131048, 132406, 133771, 135143, 136522, 139301, 140701, 149248, 153616, 155086, 156563, 158047, 164053, 165572, 167098, 176401, 179558, 182743, 184346, 185956, 187573, 189197, 194111, 199088, 200761, 202441, 207523, 214397, 219626, 221383, 224918, 226696, 228481, 230273, 232072, 233878, 237511, 239338, 241172, 244861, 246716, 250447, 252323, 257993, 259897, 263726, 265651, 271468, 273421, 277348, 279322, 283291, 285286, 287288, 289297, 295366, 303556, 307693, 311858, 313951, 316051, 318158, 320272, 322393, 324521, 326656, 335266, 339613, 346186, 352822, 361768, 366283, 368551, 375397, 377693, 386947, 389278, 396313, 398672, 403411, 410572, 417796, 420218, 422647, 425083, 427526, 432433, 434897, 442331, 444823, 447322, 452341, 454861, 459922, 462463, 470128, 475273, 483043, 485647, 493501, 501418, 514753, 520136, 522838, 528263, 530986, 533716, 536453, 541948, 544706, 550243, 553022, 561401, 567022, 569843, 578348, 581197, 584053, 586916, 592663, 607153, 610072, 612998, 615931, 621818, 630701, 639647, 642643, 651673, 654697, 657728, 660766, 669922, 672988, 679141, 685322, 694646, 697768, 707176, 719818, 722996, 726181, 729373, 732572, 735778, 745438, 751913, 755161, 761678, 771506, 778093, 784708, 798022, 801368, 811448, 818203, 848947, 852398, 855856, 859321, 862793, 866272, 876751, 887293, 905003, 919297, 922888, 926486, 933703, 937322, 940948, 944581, 970208, 973897, 977593, 981296, 988723, 992447.

Some larger examples :