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decagonal n.  and  odious n.

First numbers that belong to both sets:

1, 52, 370, 451, 637, 855, 976, 1387, 1540, 1870, 2047, 2232, 2425, 3277, 5076, 5662, 5967, 6601, 7267, 7612, 7965, 8695, 9457, 10251, 11077, 11502, 12376, 13747, 14701, 15190, 15687, 16192, 18837, 19951, 21097, 21682, 22275, 23485, 24727, 25360, 26001, 27307, 27972, 28645, 30015, 30712, 32851, 36576, 37345, 39700, 40501, 43785, 47197, 50737, 51642, 52555, 53476, 54405, 56287, 58201, 60147, 71422, 73576, 76867, 77980, 79101, 80230, 82512, 84826, 89550, 90751, 91960, 94402, 99382, 103201, 104490, 105787, 107092, 108405, 111055, 113737, 115090, 117820, 120582, 123376, 124785, 136345, 137826, 142317, 143830, 145351, 148417, 156222, 159400, 187705, 191187, 198247, 200032, 201825, 209077, 210910, 214600, 216457, 218322, 220195, 222076, 225862, 227767, 237412, 239365, 243295, 247257, 253260, 255277, 257302, 259335, 261376, 273790, 275887, 280105, 282226, 284355, 295120, 297297, 299482, 308302, 312760, 315001, 317250, 319507, 324045, 328615, 344862, 351945, 354322, 363910, 366327, 368752, 371185, 376075, 378532, 383470, 385951, 388440, 395955, 398476, 401005, 406087, 408640, 411201, 413770, 416347, 418932, 421525, 426735, 431977, 434610, 439900, 455962, 458667, 461380, 472312, 480595, 486157, 497377, 500202, 505876, 508725, 511582, 514447, 520201, 523090, 525987, 528892, 534726, 537655, 555397, 570402, 588672, 591745, 610351, 613480, 616617, 619762, 622915, 629245, 638800, 642001, 651652, 658126, 661375, 664632, 674451, 677740, 681037, 690976, 694305, 697642, 700987, 707701, 714447, 721225, 724626, 738310, 748657, 755595, 759076, 766062, 783667, 790765, 794326, 805057, 812251, 815860, 819477, 826735, 845020, 848701, 859792, 863505, 874692, 882190, 889720, 901075, 908685, 912502, 916327, 920160, 924001, 927850, 935572, 947215, 955017, 970717, 974662, 978615, 986545, 998500, 1002501, 1010527, 1022626, 1026675, 1071742, 1075887, 1096732, 1100925, 1105126, 1113552, 1122010, 1139022, 1151865, 1156162, 1164780, 1173430, 1203957, 1208350, 1212751, 1217160, 1226002, 1234876, 1239325, 1243782, 1248247, 1261690, 1266187, 1275205, 1293337, 1302451, 1307020, 1311597, 1316182, 1325376, 1339227, 1357807, 1367145, 1390630, 1395351, 1400080, 1414315, 1423845.

Some larger examples :