%N 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.
%C Probably finite. No more terms < 10^9.
%C Asked by an anonymous person on Wikipedia, December 31 2021.
%C No more terms < 10^11. - _Martin Ehrenstein_, Jan 15 2022
%H Wikipedia:Reference desk/Mathematics, <a href="https://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2021_December_31#Number_theory">Original question on Wikipedia December 31 2021</a>
%e 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.
%Y Cf. A000040, A000217, A347567.
%A _Jud McCranie_, Jan 02 2022