Formula for Central polygonal numbers is $\frac{n(n+1)}{2} + 1$, if $n=1$ or $n$ is prime, we get the new sequence $A$:
2, 4, 7, 16, 29, 67, 92, 154, 191, ...
It seems that all primes either is terms of $A$ or can be expressed by adding and subtracting distinct terms of $A$? Such as: $$ \begin{align*} &2 \\ &3=7-4 \\ &5=7-2 \\ &\cdots \\ &17=16+7-2-4\\ &\cdots \end{align*} $$ How to prove this?