First numbers that belong to both sets:
25,
65,
133,
205,
425,
785,
925,
2005,
2500,
3445,
4025,
6325,
8125,
10001,
15689,
16265,
20000,
20005,
22025,
35125,
40025,
78253,
79405,
80125,
90925,
100001,
160625,
206125,
250000,
390881,
393185,
400025,
800125,
1000001,
1358125,
1600625,
1958245,
2000005,
2004325,
2950625,
3203125,
4000025,
6415625,
7073125,
9766649,
9775865,
9868025.