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strobogrammatic n.  and  zygodrome

First numbers that belong to both sets:

11, 88, 111, 888, 1111, 6699, 8888, 9966, 11111, 88888, 110011, 111111, 118811, 660099, 661199, 666999, 668899, 880088, 881188, 888888, 990066, 991166, 998866, 999666, 1100011, 1111111, 1188811, 6600099, 6611199, 6688899, 8800088, 8811188, 8888888, 9900066, 9911166, 9988866, 11000011, 11100111, 11111111, 11188111, 11669911, 11888811, 11996611, 66000099, 66111199, 66600999, 66611999, 66669999, 66688999, 66888899, 66996699, 88000088, 88111188, 88669988, 88800888, 88811888, 88888888, 88996688, 99000066, 99111166, 99669966, 99888866, 99900666, 99911666, 99988666, 99996666, 110000011, 111000111, 111111111, 111888111, 118888811, 660000099, 661111199, 666000999, 666111999, 666888999, 668888899, 880000088, 881111188, 888000888, 888111888, 888888888, 990000066, 991111166, 998888866, 999000666, 999111666, 999888666, 1100000011, 1100110011, 1100880011, 1110000111, 1111001111, 1111111111, 1111881111, 1116699111, 1118888111, 1119966111, 1166009911, 1166119911, 1166699911, 1166889911, 1188008811, 1188118811, 1188888811, 1199006611, 1199116611, 1199886611, 1199966611, 6600000099, 6600110099, 6600880099, 6611001199, 6611111199, 6611881199, 6660000999, 6661111999, 6666009999, 6666119999, 6666699999, 6666889999, 6668888999, 6669966999, 6688008899, 6688118899, 6688888899, 6699006699, 6699116699, 6699886699, 6699966699, 8800000088, 8800110088, 8800880088, 8811001188, 8811111188, 8811881188, 8866009988, 8866119988, 8866699988, 8866889988, 8880000888, 8881111888, 8886699888, 8888008888, 8888118888, 8888888888, 8889966888, 8899006688, 8899116688, 8899886688, 8899966688, 9900000066, 9900110066, 9900880066, 9911001166, 9911111166, 9911881166, 9966009966, 9966119966, 9966699966, 9966889966, 9988008866, 9988118866, 9988888866, 9990000666, 9991111666, 9996699666, 9998888666, 9999006666, 9999116666, 9999886666, 9999966666, 11000000011, 11001110011, 11008880011, 11100000111, 11110001111, 11111111111, 11118881111, 11188888111, 11660009911, 11661119911, 11668889911, 11880008811, 11881118811, 11888888811, 11990006611, 11991116611, 11998886611, 66000000099, 66001110099, 66008880099, 66110001199, 66111111199, 66118881199, 66600000999, 66611111999, 66660009999, 66661119999, 66668889999, 66688888999, 66880008899, 66881118899, 66888888899, 66990006699, 66991116699, 66998886699, 88000000088, 88001110088, 88008880088, 88110001188, 88111111188, 88118881188, 88660009988, 88661119988, 88668889988, 88800000888, 88811111888, 88880008888, 88881118888, 88888888888, 88990006688, 88991116688, 88998886688, 99000000066, 99001110066, 99008880066, 99110001166, 99111111166, 99118881166, 99660009966, 99661119966, 99668889966, 99880008866, 99881118866, 99888888866, 99900000666, 99911111666, 99988888666, 99990006666, 99991116666, 99998886666, 110000000011, 110001100011, 110008800011, 110011110011, 110066990011, 110088880011, 110099660011, 111000000111, 111001100111, 111008800111, 111100001111, 111110011111, 111111111111, 111118811111, 111166991111, 111188881111, 111199661111, 111660099111, 111661199111, 111666999111, 111668899111, 111880088111, 111881188111, 111888888111, 111990066111, 111991166111, 111998866111, 111999666111, 116600009911, 116611119911, 116660099911, 116661199911, 116666999911, 116668899911, 116688889911, 116699669911, 118800008811, 118811118811.

Some larger examples :