[seqfan] "integers >4 which cannot be written as the sum of a nontrivial triangular number (>1) and a prime"

[Jonathan Post]

Playing on paper with pencil I think that
7, 16, 36, 42, 61, ...
is "integers >4 which cannot be written as the sum of a nontrivial
triangular number (>1) and a prime"
That's not in OEIS.  But is it correct?  And how may it be extended?