It doesn’t look as if there are a lot of other such relationships to be found. There are a few probably-coincidental simple linear relationships between consecutive numbers very near the start. There are lots of y=−x, quite a lot of 4x=4−y2, one maybe-coincidental 14−x=2−y2, one maybe-coincidental x=−4(1−y)2, some 2x=1−y2, and I’m not seeing anything else among the first 400 pairs.
[EDITED to add:] But I have only looked at relationships where all the key numbers are powers of 2; maybe I should be considering things with 5s in as well. (Or maybe it’s 2s and 10s rather than 2s and 5s.)
It doesn’t look as if there are a lot of other such relationships to be found. There are a few probably-coincidental simple linear relationships between consecutive numbers very near the start. There are lots of y=−x, quite a lot of 4x=4−y2, one maybe-coincidental 14−x=2−y2, one maybe-coincidental x=−4(1−y)2, some 2x=1−y2, and I’m not seeing anything else among the first 400 pairs.
[EDITED to add:] But I have only looked at relationships where all the key numbers are powers of 2; maybe I should be considering things with 5s in as well. (Or maybe it’s 2s and 10s rather than 2s and 5s.)