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amenable n.  and  strobogrammatic n.

First numbers that belong to both sets:

1, 8, 69, 88, 96, 101, 181, 609, 689, 808, 888, 916, 1001, 1881, 1961, 6009, 6889, 6969, 8008, 8888, 8968, 9116, 9696, 10001, 10101, 10801, 18081, 18181, 18881, 19061, 19161, 19861, 60009, 60109, 60809, 68089, 68189, 68889, 69069, 69169, 69869, 80008, 80108, 80808, 88088, 88188, 88888, 89068, 89168, 89868, 91016, 91116, 91816, 96096, 96196, 96896, 100001, 101101, 106901, 108801, 109601, 180081, 181181, 186981, 188881, 189681, 190061, 191161, 196961, 198861, 199661, 600009, 601109, 606909, 608809, 609609, 680089, 681189, 686989, 688889, 689689, 690069, 691169, 696969, 698869, 699669, 800008, 801108, 806908, 808808, 809608, 880088, 881188, 886988, 888888, 889688, 890068, 891168, 896968, 898868, 899668, 910016, 911116, 916916, 918816, 919616, 960096, 961196, 966996, 968896, 969696, 1000001, 1001001, 1008001, 1010101, 1011101, 1018101, 1060901, 1061901, 1068901, 1080801, 1081801, 1088801, 1090601, 1091601, 1098601, 1800081, 1801081, 1808081, 1810181, 1811181, 1818181, 1860981, 1861981, 1868981, 1880881, 1881881, 1888881, 1890681, 1891681, 1898681, 1900061, 1901061, 1908061, 1910161, 1911161, 1918161, 1960961, 1961961, 1968961, 1980861, 1981861, 1988861, 1990661, 1991661, 1998661, 6000009, 6001009, 6008009, 6010109, 6011109, 6018109, 6060909, 6061909, 6068909, 6080809, 6081809, 6088809, 6090609, 6091609, 6098609, 6800089, 6801089, 6808089, 6810189, 6811189, 6818189, 6860989, 6861989, 6868989, 6880889, 6881889, 6888889, 6890689, 6891689, 6898689, 6900069, 6901069, 6908069, 6910169, 6911169, 6918169, 6960969, 6961969, 6968969, 6980869, 6981869, 6988869, 6990669, 6991669, 6998669, 8000008, 8001008, 8008008, 8010108, 8011108, 8018108, 8060908, 8061908, 8068908, 8080808, 8081808, 8088808, 8090608, 8091608, 8098608, 8800088, 8801088, 8808088, 8810188, 8811188, 8818188, 8860988, 8861988, 8868988, 8880888, 8881888, 8888888, 8890688, 8891688, 8898688, 8900068, 8901068, 8908068, 8910168, 8911168, 8918168, 8960968, 8961968, 8968968, 8980868, 8981868, 8988868, 8990668, 8991668, 8998668, 9100016, 9101016, 9108016, 9110116, 9111116, 9118116, 9160916, 9161916, 9168916, 9180816, 9181816, 9188816, 9190616, 9191616, 9198616, 9600096, 9601096, 9608096, 9610196, 9611196, 9618196, 9660996, 9661996, 9668996, 9680896, 9681896, 9688896, 9690696, 9691696, 9698696, 10000001, 10011001, 10069001, 10088001.

Some larger examples :