Are there any constraints on the shape of the final grid? Can it have holes?
For instance, none of 6's neighbors require 6 to be there. It could be removed and placed on the right edge near 47 so that 53 could be added.
9 could also be removed and placed elsewhere.
Here's an infinite solution:
Code:1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 ...
3 6 9 12 15 18 21 24 27 30 33 ...