These are the sequences of even integers greater than 7 such that 100an=64an+1, in other words an2=6an+1+4. The first one I noticed is (8 10 16), that is, 1008=6410, and 10010=6416.
Here are the sequences up to 986. Some of these are long and are put on other pages. These are written in base 1000000000; that is, "509868807 91252266" is 509,868,807,091,252,266.
8 10 16 42
12
14 32 170 4816 3865642 2490531345360
18
20 66
22 80 1066 189392 5978221610 5956522269711832016 5913359591595499145281505571167104042 5827970276585748074286667660065476529979312208145367609757859954142122960
24
26 112 2090 728016
30
34 192
36
38 240
40 266 11792 23175210
44 322 17280
46 352 20650 71070416 841834005068842 118114082015041183024859870160
48
50 416 28842
52 450
54
56 522
58 560 52266
60
62 640 68266 776707792 100545832358919210
64 682 77520
68 770 98816 1627433642 441423376518897360
70 816
72
74 912
76 962 154240 3964996266
78
82 1120 209066 7284765392 8844634469413485610 13037926482922861686408992088279512016
84
86 1232 252970 10665636816
88 1290
90
92 1410
94 1472 361130 21735812816 78740926462031641642 1033355583349845803642619810400251409360 177970626940050019648139653662225502255146090982952816931752005649111049268266
96
98 1600 426666