First numbers that belong to both sets:
1,
4,
8,
9,
32,
64,
81,
100,
400,
441,
841,
900,
961,
1000,
6400,
7744,
7776,
8000,
8100,
10000,
40000,
44100,
64000,
84100,
90000,
96100,
100000,
640000,
774400,
810000,
1000000,
3200000,
4000000,
4410000,
8000000,
8410000,
8874441,
9000000,
9610000,
9853321,
10000000,
64000000,
77440000,
81000000,
100000000,
400000000,
441000000,
777600000,
841000000,
887444100,
900000000,
961000000,
985332100,
999887641,
1000000000,
6400000000,
7744000000,
8000000000,
8100000000,
10000000000,
40000000000,
44100000000,
64000000000,
84100000000,
88744410000,
90000000000,
96100000000,
98533210000,
99988764100,
100000000000,
320000000000,
640000000000,
774400000000,
810000000000,
1000000000000,
4000000000000,
4410000000000,
8000000000000,
8410000000000,
8874441000000,
9000000000000,
9610000000000,
9853321000000,
9998876410000,
10000000000000.