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odious n.  and  strobogrammatic n.

First numbers that belong to both sets:

1, 8, 11, 69, 88, 181, 689, 818, 906, 916, 986, 1001, 1691, 1881, 1961, 6009, 6699, 8008, 9006, 9116, 9966, 10101, 11111, 11811, 16091, 16891, 60009, 60809, 61019, 61119, 61819, 66199, 66899, 68089, 68889, 69069, 69169, 80108, 80808, 81118, 81818, 86898, 88188, 88888, 89068, 89168, 89868, 90006, 90106, 90806, 91016, 96096, 96896, 98086, 98186, 99066, 99166, 99866, 100001, 109601, 119611, 161191, 166991, 168891, 169691, 181181, 188881, 190061, 191161, 199661, 609609, 610019, 611119, 618819, 660099, 661199, 669699, 800008, 801108, 806908, 811118, 816918, 819618, 860098, 868898, 881188, 886988, 899668, 900006, 901106, 908806, 910016, 911116, 919616, 960096, 961196, 966996, 969696, 980086, 981186, 989686, 991166, 998866, 1008001, 1010101, 1061901, 1080801, 1081801, 1090601, 1098601, 1108011, 1110111, 1160911, 1161911, 1168911, 1180811, 1600091, 1610191, 1661991, 1800081, 1801081, 1811181, 1818181, 1880881, 1888881, 1890681, 1898681, 1901061, 1908061, 1968961, 1981861, 6008009, 6060909, 6061909, 6068909, 6080809, 6081809, 6090609, 6100019, 6101019, 6110119, 6118119, 6161919, 6180819, 6181819, 6610199, 6661999, 6691699, 6698699, 6800089, 6811189, 6818189, 6861989, 6880889, 6888889, 6890689, 6898689, 6900069, 6908069, 6911169, 6918169, 6968969, 6980869, 6990669, 8011108, 8018108, 8080808, 8081808, 8090608, 8100018, 8108018, 8110118, 8118118, 8181818, 8190618, 8600098, 8611198, 8618198, 8668998, 8681898, 8688898, 8691698, 8698698, 8811188, 8818188, 8880888, 8890688, 8891688, 8900068, 8910168, 8911168, 8918168, 8960968, 8968968, 8980868, 8991668, 9000006, 9008006, 9011106, 9018106, 9080806, 9091606, 9098606, 9101016, 9108016, 9111116, 9118116, 9160916, 9161916, 9190616, 9198616, 9610196, 9611196, 9618196, 9668996, 9688896, 9698696, 9800086, 9811186, 9860986, 9861986, 9868986, 9888886, 9891686, 9898686, 9901066, 9908066, 9988866, 9990666, 9991666, 9998666, 10000001, 10011001, 10069001, 10096001, 10100101, 10188101, 10196101, 10669901, 10696901, 10800801, 10811801, 10911601, 10969601, 10988601, 10996601, 11011011, 11188111, 11196111, 11600911, 11669911, 11688911, 11800811, 11888811, 11896811, 11900611, 11996611, 16088091, 16100191, 16196191, 16611991, 16696991, 16800891, 16888891, 16896891, 16911691, 16969691, 16996691, 18069081, 18100181, 18196181, 18669981, 18800881, 18869881, 18888881, 18996681, 19000061, 19069061, 19100161, 19169161.

Some larger examples :