Positive integers which are not twice a positive triangular number and cannot be written as twice a positive triangular number plus an odd prime or twice a positive triangular number plus twice an odd prime.
5 is NOT a term because 5 is not twice a triangular number and it can be written as 2*1+3, where 1 is a triangular and 3 is an odd prime. However, 10 is a term because it cannot be written in this way.