First numbers that belong to both sets:
11,
1177711,
7722277,
7733377,
331111133,
772222277,
779999977,
992222299,
995555599,
11006660011,
11117771111,
11119991111,
11155555111,
11188888111,
11442224411,
11447774411,
11663336611,
11668886611,
11775557711,
11776667711,
11779997711,
11991119911,
11992229911,
33117771133,
33119991133,
33224442233,
33445554433,
33448884433,
33553335533,
33557775533,
77006660077,
77009990077,
77111111177,
77119991177,
77332223377,
77334443377,
77337773377,
77339993377,
77448884477,
77663336677,
77779997777,
77991119977,
99113331199,
99222222299,
99227772299,
99443334499,
99448884499,
99449994499,
99555555599,
99558885599,
99883338899,
99888888899,
1100011100011,
1100066600011,
1100999990011,
1111188811111,
1111666661111,
1112233322111,
1112255522111,
1112277722111,
1114411144111,
1118866688111,
1118888888111,
1122200022211,
1122777772211,
1133300033311,
1133344433311,
1144111114411,
1144466644411,
1155444445511,
1155500055511,
1155599955511,
1166688866611,
1177788877711,
1188811188811,
1199999999911,
3300222220033,
3300777770033,
3300888880033,
3331100011333,
3331177711333,
3332211122333,
3332255522333,
3334477744333,
3335555555333,
3335599955333,
3338800088333,
3338833388333,
3344666664433,
3355111115533,
3366777776633,
3388777778833,
3388999998833,
7700222220077,
7711444441177,
7711999991177,
7722111112277,
7722888882277,
7733300033377,
7733666663377,
7744466644477,
7744499944477,
7755500055577,
7755544455577,
7755599955577,
7766555556677,
7766633366677,
7771166611777,
7772255522777,
7774422244777,
7775522255777,
7775588855777,
7777111117777,
7777333337777,
7777788877777,
7777799977777,
7778844488777,
7778866688777,
7778888888777,
7788777778877,
7788844488877,
7788866688877,
7799222229977,
7799988899977,
7799999999977,
9922666662299,
9933777773399,
9955333335599,
9955666665599,
9966111116699,
9966888886699,
9988111118899,
9988333338899,
9991111111999,
9994433344999,
9997722277999,
9998811188999,
9998855588999,
110000888000011,
110009999900011,
110044222440011,
110044333440011,
110044444440011,
110066777660011,
110066999660011,
110099333990011,
110099444990011,
110099666990011,
111004444400111,
111008888800111,
111100111001111,
111100333001111,
111133444331111,
111133777331111,
111133888331111,
111166888661111,
111188111881111,
111188222881111,
111188888881111,
111199999991111,
111220000022111,
111337777733111,
111440000044111,
111779999977111,
111883333388111,
111991111199111,
112222111222211,
112222666222211,
112277111772211,
112277555772211,
113300111003311,
113300666003311,
113311888113311,
113330000033311,
113344222443311,
113377333773311,
113399888993311,
114400444004411,
114422111224411,
114422222224411,
114422333224411,
114433444334411,
114433777334411,
114455777554411,
114466555664411,
114466888664411,
114488666884411,
114488999884411,
114499111994411,
114499999994411,
115522444225511,
115522666225511,
115552222255511,
115555444555511,
115556666655511,
115577111775511,
116600111006611,
116600666006611,
116633888336611,
116633999336611,
116644666446611,
116660000066611,
116663333366611,
116666666666611,
116666888666611,
116677888776611,
116699999996611,
117700888007711,
117733111337711,
117733555337711,
117755111557711,
117755444557711,
117775555577711,
117779999977711,
117799111997711,
118811222118811,
118811444118811,
118811666118811,
118855333558811,
118855444558811,
118855555558811,
118855888558811,
118877444778811,
118877777778811,
118888666888811,
118888999888811,
119900111009911,
119911666119911,
119911888119911,
119911999119911,
119933666339911,
119944333449911,
119944999449911,
119966555669911,
119977333779911,
330011111110033,
330044666440033,
330055999550033,
330077111770033,
330077777770033,
330088666880033,
331111111111133,
331111555111133,
331114444411133,
331133333331133,
331133888331133,
331144111441133,
331144777441133,
331166666661133,
331166999661133,
331177111771133,
331199777991133,
332200333002233,
332222111222233,
332255222552233,
332255777552233,
332266333662233,
332266666662233,
332288888882233,
332299333992233,
333110000011333,
333322333223333,
333344444443333,
333355999553333,
333377222773333,
333377333773333,
333377888773333,
333388777883333,
333662222266333,
333668888866333,
333773333377333,
333889999988333,
334400333004433,
334411222114433,
334411777114433,
334411888114433,
334433666334433,
334444999444433,
334466333664433,
334466777664433.
Some larger examples :
997733666337799,
997744222447799,
997744555447799,
997766555667799,
997777888777799,
997777999777799,
997799444997799,
997799888997799,
998800555008899,
998833777338899,
998866333668899,
998899333998899,
999002222200999,
999113333311999,
999226666622999,
999779999977999,
999911777119999,
999922222229999,
999944222449999,
999955444559999.