First numbers that belong to both sets:
1,
25,
49,
81,
121,
289,
361,
529,
625,
841,
961,
1089,
1225,
1521,
1681,
1849,
2401,
2601,
3025,
3481,
4225,
4489,
5041,
5625,
5929,
6241,
7225,
7569,
7921,
8281,
9025,
9409,
10201,
10609,
12769,
13689,
14641,
15625,
16129,
16641,
17161,
18225,
19321,
20449,
21025,
21609,
22201,
23409,
24649,
26569,
27889,
28561,
29929,
30625,
32041,
32761,
34225,
35721,
37249,
38809,
40401,
43681,
46225,
47089,
49729,
50625,
51529,
52441,
53361,
55225,
57121,
59049,
61009,
63001,
66049,
67081,
69169,
71289,
73441,
75625,
77841,
80089,
81225,
88209,
90601,
93025,
94249,
95481,
97969,
101761,
104329,
105625,
108241,
112225,
116281,
117649,
119025,
121801,
123201,
124609,
126025,
127449,
131769,
139129,
140625,
143641,
146689,
148225,
151321,
154449,
156025,
160801,
164025,
165649,
167281,
177241,
178929,
180625,
184041,
185761,
187489,
189225,
192721,
198025,
201601,
208849,
218089,
219961,
223729,
229441,
231361,
235225,
237169,
243049,
247009,
251001,
255025,
259081,
261121,
263169,
265225,
269361,
273529,
277729,
281961,
288369,
290521,
294849,
297025,
299209,
301401,
303601,
312481,
314721,
316969,
319225,
321489,
323761,
326041,
330625,
335241,
337561,
339889,
342225,
346921,
354025,
356409,
361201,
363609,
373321,
375769,
383161,
388129,
395641,
400689,
403225,
405769,
413449,
416025,
418609,
423801,
436921,
439569,
442225,
444889,
447561,
450241,
452929,
458329,
461041,
463761,
466489,
474721,
477481,
480249,
485809,
488601,
491401,
497025,
511225,
516961,
525625,
528529,
534361,
543169,
552049,
555025,
558009,
567009,
570025,
579121,
585225,
591361,
597529,
603729,
606841,
616225,
619369,
625681,
628849,
635209,
638401,
644809,
648025,
654481,
664225,
670761,
680625,
690561,
697225,
700569,
720801,
734449,
737881,
755161,
758641,
765625,
772641,
776161,
790321,
793881,
801025,
804609,
811801,
815409,
822649,
826281,
840889,
844561,
848241,
851929,
855625,
859329,
863041,
866761,
870489,
881721,
889249,
900601,
904401,
908209,
923521,
927369,
931225,
935089,
938961,
962361,
970225,
974169,
982081,
990025,
1002001,
1006009,
1014049,
1022121,
1030225,
1038361,
1050625,
1054729,
1062961.
Some larger examples :
996096721,
996349225,
996475489,
996601761,
996854329,
997233241,
997612225,
997864921,
997991281,
998117649,
998496801,
998623201,
998876025,
999002449,
999128881,
999381769,
999508225,
999634689,
999761161,
999887641.