First numbers that belong to both sets:
1,
9,
25,
49,
169,
289,
361,
529,
729,
841,
961,
1369,
2209,
3481,
3721,
3969,
4761,
5041,
7921,
9409,
9801,
10609,
12321,
15129,
17689,
20449,
21609,
24025,
24649,
32041,
32761,
35721,
36481,
42025,
42849,
43681,
50625,
52441,
53361,
65025,
66049,
73441,
75625,
77841,
83521,
87025,
90601,
99225,
110889,
113569,
121801,
126025,
128881,
130321,
142129,
159201,
167281,
172225,
175561,
178929,
182329,
185761,
203401,
207025,
233289,
239121,
261121,
292681,
294849,
312481,
323761,
326041,
332929,
339889,
373321,
393129,
395641,
398161,
413449,
416025,
418609,
431649,
469225,
474721,
483025,
491401,
508369,
516961,
528529,
570025,
579121,
606841,
628849,
644809,
664225,
680625,
683929,
697225,
707281,
714025,
724201,
731025,
765625,
772641,
776161,
790321,
808201,
863041,
877969,
881721,
900601,
904401,
954529,
1014049,
1018081,
1042441,
1046529,
1054729,
1100401,
1104601,
1125721,
1129969,
1168561,
1243225,
1283689,
1288225,
1297321,
1394761,
1447209,
1452025,
1471369,
1485961,
1545049,
1550025,
1555009,
1635841,
1661521,
1687401,
1692601,
1703025,
1713481,
1841449,
1874161,
1918225,
1962801,
1974025,
1979649,
1996569,
2002225,
2024929,
2036329,
2047761,
2117025,
2122849,
2152089,
2157961,
2175625,
2223081,
2241009,
2247001,
2325625,
2331729,
2368521,
2449225,
2455489,
2468041,
2474329,
2544025,
2563201,
2627641,
2634129,
2725801,
2739025,
2758921,
2778889,
2819041,
2839225,
2879809,
2907025,
2913849,
2920681,
2954961,
3010225,
3038049,
3052009,
3087049,
3108169,
3122289,
3164841,
3243601,
3286969,
3308761,
3323329,
3352561,
3396649,
3411409,
3463321,
3560769,
3629025,
3636649,
3690241,
3783025,
3822025,
3869089,
3884841,
3908529,
3916441,
4036081,
4068289,
4092529,
4116841,
4133089,
4141225,
4157521,
4173849,
4231249,
4255969,
4289041,
4297329,
4322241,
4338889,
4389025,
4473225,
4498641,
4566769,
4583881,
4592449,
4601025,
4652649,
4756761,
4782969,
4897369,
4950625,
4977361,
5004169,
5013121,
5040025,
5139289,
5202961,
5239521,
5349969,
5414929,
5499025,
5536609,
5583769,
5602689,
5621641,
5745609,
5764801,
5968249,
6027025,
6086089,
6125625,
6245001,
6365529,
6456681,
6466849,
6487209,
6497401,
6599761,
6630625,
6661561,
6723649,
6796449,
6859161,
6880129,
6901129,
6996025,
7017201,
7038409,
7091569,
7144929,
7166329,
7219969,
7230721,
7241481,
7284601,
7295401,
7317025,
7349521.
Some larger examples :
8637721,
8649481,
8673025,
8720209,
8743849,
8874441,
8958049,
9042049,
9054081,
9126441,
9162729,
9259849,
9320809,
9369721,
9381969,
9566649,
9616201,
9728161,
9928801,
9941409.