First numbers that belong to both sets:
13,
19,
29,
59,
103,
109,
199,
311,
433,
599,
809,
811,
1033,
1699,
1933,
1999,
2027,
2111,
2999,
3299,
4799,
5009,
5099,
6199,
6299,
7333,
8009,
8599,
8999,
10009,
10037,
10303,
10333,
13999,
17027,
22037,
22111,
23027,
25999,
26111,
28111,
30011,
49333,
55333,
58111,
60101,
61333,
68111,
70999,
79999,
80909,
85333,
86111,
94111,
101111,
101999,
131111,
160033,
164999,
170099,
170101,
179999,
184999,
230999,
247999,
268999,
272999,
280099,
293999,
301333,
301999,
313333,
322999,
326999,
328333,
331999,
379999,
389999,
410999,
419999,
430909,
443999,
448999,
450101,
496999,
500909,
511111,
512999,
524999,
536999,
580303,
611111,
616999,
620909,
652999,
659999,
662999,
670099,
691111,
694999,
710909,
721111,
733333,
769999,
773999,
781999,
788999,
794999,
800999,
818999,
820909,
850303,
868999,
880303,
880909,
890999,
904999,
907999,
910099,
920999,
932999,
970999,
973333,
980909,
989999,
1000037,
1000039,
1000429,
1003003,
1003367,
1100041,
1171111,
1273333,
1363333,
1381111,
1393333,
1420303,
1480909,
1483333,
1500041,
1600813,
1603333,
1609999,
1693333,
1841111,
2000351,
2002331,
2003861,
2025641,
2030909,
2051111,
2200813,
2202439,
2390909,
2480909,
2623333,
2710909,
2810909,
2833333,
3001001,
3005291,
3043333,
3149999,
3181111,
3271111,
3350909,
3402439,
3481111,
3740909,
3800369,
4000037,
4000039,
4000693,
4100909,
4121111,
4139999,
4211111,
4231111,
4270909,
4441111,
4500271,
4520909,
4580909,
4679999,
4720909,
4900123,
4940909,
5000111,
5041111,
5110909,
5201111,
5381111,
5502439,
5539999,
5551111,
5570909,
5800369,
6000481,
6011111,
6013333,
6080909,
6089999,
6223333,
6260909,
6400369,
6490909,
6500369,
6569999,
6613333,
6650909,
6671111,
6689999,
6730909,
6751111,
6760909,
6781111,
6811111,
6851111,
6941111,
6959999,
7031111,
7040909,
7047619,
7271111,
7279999,
7351111,
7459999,
7519999,
7550909,
7589999,
7639999,
7730909,
7751111,
7861111,
7900813,
7990909,
8000099,
8000117,
8009009,
8071111,
8170909,
8291111,
8300909,
8351111,
8609999,
8659999,
8680909,
8731111,
8819999,
8849999,
8863333,
8959999,
8981111,
9061111,
9239999,
9371111,
9451111,
9829999,
9929999,
9943333,
10001443,
10002439,
10003003,
10153333,
10219999,
10300271,
10339999,
10513333,
10543333,
10579999,
10709999,
11000111,
11069999,
11089999,
11593333,
11602439,
11623333,
11629999,
11719999,
11869999.
Some larger examples :
982033333,
983008547,
984133333,
985111111,
986911111,
987211111,
987433333,
988001221,
989010101,
989012987,
991001443,
993011111,
993037037,
993511111,
997001221,
998002331,
998002849,
998025641,
998047619,
999311111.