First numbers that belong to both sets:
1,
7,
55,
616,
3553,
4774,
60606,
848848,
4615164,
5400045,
6050506,
7165445617,
62786368726,
65331413356,
73665056637,
91120102119,
345546645543,
365139931563,
947927729749,
3646334336463,
7111015101117,
717685292586717.