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gapful n.  and  strobogrammatic n.

First numbers that belong to both sets:

1001, 1111, 1881, 6969, 8008, 8888, 9696, 11011, 69069, 88088, 96096, 100001, 101101, 108801, 110011, 111111, 118811, 166991, 180081, 181181, 188881, 199661, 690069, 696969, 800008, 808808, 880088, 888888, 918816, 960096, 969696, 1100011, 1610191, 1808081, 1861981, 1891681, 1910161, 6898689, 6900069, 8800088, 9191616, 9600096, 9688896, 10000001, 10011001, 10088001, 10100101, 10111101, 10188101, 10669901, 10800801, 10811801, 10888801, 10996601, 11000011, 11011011, 11088011, 11100111, 11111111, 11188111, 11669911, 11800811, 11811811, 11888811, 11996611, 16096091, 16196191, 16600991, 16611991, 16688991, 16896891, 18000081, 18011081, 18088081, 18100181, 18111181, 18188181, 18669981, 18800881, 18811881, 18888881, 18996681, 19069061, 19169161, 19869861, 19900661, 19911661, 19988661, 69000069, 69069069, 69696969, 80000008, 80011008, 80088008, 80800808, 80811808, 80888808, 80996608, 88000088, 88011088, 88088088, 88800888, 88811888, 88888888, 88996688, 89169168, 96000096, 96096096, 96969696, 100101001, 101609101, 101818101, 101906101, 108689801, 108986801, 110000011, 111101111, 116609911, 116818911, 116906911, 118181811, 118808811, 119609611, 119818611, 119906611, 161000191, 166101991, 168080891, 168619891, 168916891, 169101691, 180888081, 181010181, 186111981, 188101881, 189111681, 191000161, 196101961, 198080861, 198619861, 198916861, 199101661, 600111009, 608818809, 610619019, 669111699, 689101689, 690000069, 696906969, 800181008, 800808008, 808010808, 880000088, 888181888, 888808888, 889609688, 889818688, 889906688, 891080168, 891619168, 891916168, 896181968, 896808968, 910010016, 918906816, 919619616, 960000096, 960888096, 968080896, 969609696, 1000000001, 1000110001, 1000880001, 1001001001, 1001111001, 1001881001, 1006699001, 1008008001, 1008118001, 1008888001, 1009966001, 1010000101, 1010110101, 1010880101, 1011001101, 1011111101, 1011881101, 1016699101, 1018008101, 1018118101, 1018888101, 1019966101, 1060960901, 1061961901, 1066009901, 1066119901, 1066889901, 1068968901, 1080000801, 1080110801, 1080880801, 1081001801, 1081111801, 1081881801, 1086699801, 1088008801, 1088118801, 1088888801, 1089966801, 1090690601, 1091691601, 1098698601, 1099006601, 1099116601, 1099886601, 1100000011, 1100110011, 1100880011, 1101001011, 1101111011, 1101881011, 1106699011, 1108008011, 1108118011, 1108888011, 1109966011, 1110000111, 1110110111, 1110880111, 1111001111, 1111111111, 1111881111, 1116699111, 1118008111, 1118118111, 1118888111, 1119966111, 1160960911, 1161961911, 1166009911, 1166119911, 1166889911, 1168968911, 1180000811, 1180110811, 1180880811, 1181001811, 1181111811, 1181881811, 1186699811, 1188008811, 1188118811, 1188888811, 1189966811, 1190690611, 1191691611, 1198698611, 1199006611, 1199116611, 1199886611, 1600690091, 1601691091, 1608698091, 1609006091, 1609116091, 1609886091, 1610690191, 1611691191, 1618698191, 1619006191, 1619116191, 1619886191, 1660000991, 1660110991, 1660880991, 1661001991, 1661111991, 1661881991, 1666699991, 1668008991.

Some larger examples :