First numbers that belong to both sets:
1,
441,
2809,
3481,
6889,
11881,
13689,
17689,
24025,
25921,
34969,
47089,
47961,
56169,
72361,
78961,
95481,
106929,
114921,
120409,
127449,
154449,
184041,
196249,
203401,
346921,
356409,
390625,
393129,
400689,
405769,
469225,
585225,
616225,
680625,
765625,
779689,
950625,
1010025,
1104601,
1108809,
1147041,
1168561,
1194649,
1279161,
1320201,
1540081,
1595169,
1682209,
1687401,
1703025,
1830609,
1912689,
1934881,
1946025,
2140369,
2229049,
2247001,
2505889,
2582449,
2621161,
2640625,
2653641,
2679769,
2719201,
2725801,
2900209,
2941225,
3101121,
3222025,
3448449,
3545689,
3728761,
3924361,
3980025,
4028049,
4397409,
4447881,
4566769,
4809249,
5067001,
5121169,
5331481,
5405625,
5508409,
5517801,
5583769,
6335289,
6345361,
6385729,
6466849,
6806881,
6890625,
6911641,
6943225,
7134241,
7177041,
7198489,
7230721,
7284601,
7800849,
8116801,
8381025,
8590761,
8602489,
8661249,
8755681,
8814961,
8826841,
8946081,
9090225,
9162729,
9443329,
9504889,
9690769.