https://oeis.org/A395338
There appear to be two problems with this sequence:
1. There are missing terms. For example, 37 should be a member of this sequence because 37^2 = 1369 = 1 + 36 + 9
2 There are missing terms that allow duplicates. For example, 107 should be a member of this sequence because 107^2 = 11449 = 1 + 1 + 4 + 4 + 9
This sequence could be saved (I think) by renaming it to Primes whose square is a concatenation of at exactly 2 distinct strictly increasing nonzero squares.
I think this issue occurs because the author used combinations (which catches 223^2 = 49729 = 4 + 9 + 729) instead of permutations (which misses 37^2 because the primes are out of order).
Thoughts on whether to change the definition or add more terms?