First numbers that belong to both sets:
13,
111,
133,
211,
1333,
2163,
2863,
3081,
3193,
10101,
10303,
13111,
49063,
169333,
1001001,
1003003,
1021111,
1090981,
2523333,
4471111,
4811443,
5164257,
7014553,
7035757,
8800123,
16293333,
22302007,
24517353,
25275757,
25517653,
33657403,
46015873,
50701521,
70015057,
73093951,
80811111,
100010001,
100030003,
107817073,
113710233,
183020313,
241010101,
254833333,
269206057,
309003663,
559015093,
570039501,
832351351,
997833333,
1002007371,
1024992241.